(written from a Production point of view)
Though only fleetingly depicted in Star Trek: The Motion Picture, the long range shuttle became a fan-favorite, as it was the very first Vulcan starship design ever seen in the franchise. In retrospect, however, that was only partly true, because its designers intended it to be a Vulcan/Federation hybrid.
The long range shuttle was a co-design by Andrew Probert and Richard Taylor, "The bridge [of the USS Enterprise] was designed so that the Vulcan shuttle could actually dock with it. The Vulcan shuttle was also another model that Andy and I designed and was kind of a takeoff of a catamaran. We kept in mind its function in that part of it was going to have to detach from the warp sled and dock with the Enterprise. I had to design a shape that was going to be able to physically dock with the docking ring behind the bridge; so anything that had too much height wouldn’t work and again, according to Roddenberry, it had to have a 12 foot in diameter door.", Taylor explained.  Probert recounted, "The script called for a shuttlecraft with warp-drive capability. Gene [Roddenberry] wanted the craft to have large warp-drive nacelles, designed to recall the old Starfleet technology. For personnel transfer, the shuttle was required to hard-dock with the USS Enterprise. As was brought out in the TV series, intraship beaming was extremely hazardous. My original sketches included the configuration–almost exactly–that we finally settled on, after many tests, which Gene liked even though it did not confirm to his original idea. I reasoned that the size of the warp engines made a hard-docking impossible, so we needed a warp-drive sled and basic shuttlecraft. I did a quick sketch to show how it would operate." (Starlog, issue 32, p. 29) Elaborating on this last notion, Probert has remarked, "In working out the design, though, I couldn't create a configuration with which I was really comfortable with until finally coming up with the idea of a large shuttle with removable warp engines, which quickly evolved into a "warp sled". The shuttle could now park its sled at some distance from a destination and simply maneuver the remaining distance to dock. I never would have imagined, however, the Trumbull–inspired "half gainer" that the ship and its Vulcan pilots performed during the docking approach." (Starlog photo guidebook Special Effects, vol. 5, p. 94)
According to later Probert interviews:
"In the script, this was a shuttle with "long-range" capabilities. Gene wanted it to have (relatively) huge warp engines to indicate how it could reach the Enterprise quickly. Starting with the original TOS shuttlecraft design, I visually peeled it down to its basic cabin and then started updating that, adding (at first) large TOS-style warp engines. The problem I was fighting was how to hard-dock with the Enterprise (an unexplained requirement overriding the transporters) while keeping those large engines out of the way. Sketching extended warp engine pylons, to help solve that problem, it occurred to me that those extensions and warp engines could be detachable during the docking process and the idea of a separate Warp Sled soon came to mind. From that point, it was a matter of refining the details and, since this was to be a Vulcan Shuttle, many of those details were derived from the Vulcan society itself. I observed, in the TOS episode #30: "Amok Time", a six-sided-diamond shape as part of their motif, especially in the ceremonial gong at the center of the featured arena. I applied this motif to various parts of the shuttle as well as using it as a cross section for the new warp engines. "The Vulcan shuttle is actually a Starfleet shuttle, co-designed with Vulcan engineers. That's why it has subtle repetitions of that ceremonial 'gong' shape we saw in "Amok Time". Anyway, my thinking was those new ships would have the same warm gray tonalities that the Galileo-type shuttles had and they would be the new standard shuttle. They would be more squat and smaller because they had to fit within the decks of the starships, but yeah, those were hopeful replacements. That long-range shuttle, though, is actually my favorite design in the movie." 
In regard to his notion of the design being a Federation/Vulcan hybrid, Probert has later specified, "The back-story in my mind at the time was that the shuttlecraft itself was a Starfleet design, while the warp sled would be contributed through the efforts of the Vulcan Space Authorities."  At the time, Probert even envisioned the shuttle part coming in two different sizes. A design sketch of 3 May 1979 specified a smaller forty feet "Starfleet-Standard-Shuttle" and a nearly one and a half larger "Starfleet-Long range-Shuttle" as the one to be attached to the warp sled.  Probert explained, "When I was asked for ideas on the Enterprise cargo decks, part of those ideas included new hanger deck spaces where one would logically expect to see shuttlecraft. Since the larger long-range shuttle had already been designed, I thought it made sense to have the Enterprise shuttles look the same, although smaller, to fit the spaces below deck. Logically if we were updating the Enterprise, the shuttles should be updated as well. Someone disagreed with that, of course, providing us all with a totally empty area back there." 
While designing the long range shuttle, Probert did not envision the craft having any secondary entrances or exits. He later noted, "I would change that today." The circular door on the rear of the craft had to be of the same proportions as the docking collar of the Enterprise, since that fitting was intended to be a universal connection.  Probert also made sure the docking collar matched up with the one seen on the travel pod, "In the case of the long-range shuttlecraft (Vulcan Shuttle), there is a small airlock adjoining it’s docking ring but the doors are the same as the Pod’s. LR Shuttles also have top & bottom emergency hatches.", in the process somewhat contradicting his earlier remark of the shuttle not having secondary entrances.
Probert referred to only the upper part of the craft's two sections as being the shuttle, calling the lower section the "warp sled"; he conceived the latter as having warp capability, equipped with both warp and impulse engines. However, this distinction is not made on screen and both portions of the craft are only ever shown traveling at slower than warp speeds (though the shuttle's name implies that the craft was capable of regularly sustaining warp to traverse long distances). Probert did not imagine the cabin section as having the ability to travel at warp or even near-light velocities, with that compartment's only intended method of travel being reaction control thrusters, which Probert included on the section's corners. Despite the slowness of the upper module, Probert envisioned it – in accordance with his wishes that the long range shuttle become the new standard shuttlecraft for Star Trek – as being capable of traveling between space and the surfaces of planets. To this end, the Surak's landing pads were marked with reddish coloring meant to be from Vulcan soil. "But when you're rushed through production to do stuff, you overlook a few things, and the problem there would have been how do you get it off the planet with only RCS thrusters...." explained Probert. "It's conceivable that it would have its own primary power system in addition to the RCS system, but I hadn't been able to think that far, and it was simply a proposal."  In regard to the shuttle's perceived absence of windows, Probert commented, "At the time, I was intrigued by the idea of total instrument flying. Certainly 200 ears from now such technology will be commonplace. And since the craft is designed to enter an atmosphere, I conceived a wedge nose to facilitate entry. The sled, incidentally, parks relative to the Enterprise and automatically keeps station with it." (Starlog, issue 32, pp. 29-30) Refining his thought processes Probert added years later, "It's true, there is only a heat shield on the front, but this shuttle has always had those side windows along with one on the back. The tall windows were designed that way in order for travelers of any eye-level height to see out. The same reasoning is behind the longer windows on the Enterprise-D, which followed years later."
Probert was the one who came up with the name of the only one seen long range shuttle in the franchise, Surak, "I remembered the name from an old Star Trek episode. Surak was the equivalent of our Abraham Lincoln in "The Savage Curtain"." (Starlog, issue 32, p. 29) Probert also planned for long range shuttles to be included in a matte painting of the cargo bay, though this plan went unrealized, as shuttles were entirely excluded from the final painting as ultimately used. 
Paramount Pictures applied for, and received two design patents from the US Patent and Trademark Office for the design. The first, D259889, tendered by the studio on 13 April 1979 and issued on 14 July 1981, concerned the entire assembly of shuttle and sled. The second, D263727, tendered on 7 May 1979 and issued on 6 April 1982, only concerned the shuttle part of the design. In both cases called a "toy spaceship" for purposes of the patent application, as they were not real spaceships, it seemed odd that two patents were issued for one design. This however, may have stemmed from the original intent of having two differently sized shuttles, considering the fact that the second patent was tendered only four days after Probert submitted his two sizes design. In both cases Probert was, discounting Taylor's input, mentioned as sole inventor. The patents, when issued, were valid for fourteen years.
Physical studio model
The studio model of the Surak was eventually built at Magicam/Astra Image Corporation. Its primary builder was Magicam's Tom Pahk. (American Cinematographer, February 1980, pp. 152, 179) The model was filmed on one of Douglas Trumbull's stages at Future General Corporation. (The Making of Star Trek: The Motion Picture, p. 206)
The paint scheme on the model was not only designed, but also partly applied by Probert himself, as he added weathering, "The Robert Abel [sic] model builders did an amazing job, from fabrication to painting. After each was all finished & documented, I got to throw in my two cents worth by adding 'weathering' to a couple of the miniatures." As to the paint scheme Probert has further stated, "So, when considering a color for the Vulcan-based long-range shuttle, I knew that I did not want yet another boring-grey space ship. But I did consider what grey would like in the red Vulcan atmosphere, and a kind of magenta or grey-pink color came to mind. That ended up being our base color, accented with various shades of muted purples. That might sound a bit odd at first, but it really looked great." (Starlog photo guidebook Special Effects, vol. 5, pp. 95-96) Unfortunately for Probert, his carefully designed color scheme for the Surak did not come across on-screen as intended. In its very first appearance, due to post-production editing, it had a coppery appearance, very much reinforced by the depictions on period merchandise, such as the box art of the AMT model kit no. S972, and the 1979 Star Trek: The Motion Picture trading cards set from Topps. Even the 2001 DVD Director's Edition only partially corrected the color scheme of the Surak.
When confronted with the footage, Probert himself was aghast, "Unfortunately, in the movie business, a selectively "collaborative" medium, once a miniature leaves the influence of its designer it is subject to indiscreet "editing" by those who are uncomfortable when confronted with thinking that rises beyond mediocrity. Consequently, someone in that group made the decision to filter out or neutralize our unconventional coloring in favor of the more "acceptable" shades of boring-grey; something that would come up again. [Note: Probert is referring to the color scheme he designed for the six-foot Enterprise-D model.] (Starlog photo guidebook Special Effects, vol. 5, p. 96) Having made the remark in 1996, Probert's anger had not abated in 2009 when he further commented, "More like shocked... and then angry at how supposedly "creative" people can be so un-creative at times.", further affirming his conviction that it was all done on purpose, "These people can shoot every color there is, so, yes, it was intentionally compromised... providing another example of that Hollywood "collaboration" process."
The model of the long-range shuttle was reported to have been on the set for the Starfleet Officers' Lounge in Star Trek III: The Search for Spock, though it does not appear on screen in that film. (Star Trek III: The Search for Spock (Special Edition) DVD-special feature, "text commentary")
The actual studio model itself has not been present in either the 2006-2008 wave of Star Trek auctions, nor the various exhibition tours of the 1990s and the 2000s. Still, considered a popular design, the model has been released by the studio in the 1980s for public relations purposes, appearing in various period conventions. The very last time the model was sighted was at the last Equicon '88 Science Fiction Convention of 1-3 April 1988, held in Los Angeles. It has been missing ever since, rumored to have been stolen on that occasion. 
Other physical models
The display model that appeared as set dressing in the episodes "Too Short a Season", "Symbiosis", and "The Dauphin", was an unmodified AMT model kit no. S972. The mere existence of the model was proof of the popularity of the design among fans, as it was the only truly new model kit released in 1979 that was not a revision of previously established Star Trek designs. In effect, when AMT was rebooted in 2008/2009 under the Round 2 LLC umbrella, it was the third model kit to be re-released, having received a full revision, for which original designer Andrew Probert was called in as a consultant.
Another AMT model was seen in the licensed Star Trek: Ships of the Line (2003) calendar, which was photographed by Daren Dochterman and composited into his otherwise CGI March spread.  The spread was reproduced in the 2006/2014 book derivatives, and has been one of the very few official print representations of the design outside the film proper references.
Only featured in The Motion Picture, no CGI model was ever deemed necessary for any franchise purposes afterwards as no further live-action production use had been called upon, so none had been forthcoming ever since. However, that was until 2020 when the magazine/display model Star Trek: The Official Starships Collection partwork Project Manager Ben Robinson decided to include the design in his "Special Edition"" side-collection.
The translation of the design into a full digital version, Robinson entrusted to long-time collection collaborator Rob Bonchune,  who, incidentally, had been a major collaborator on the 2001 Director's Edition version of the film when he was co-responsible for much of the re-imagined (digital) visual effects while in the employ of Foundation Imaging. (Star Trek: The Official Starships Collection, issue SP21, March 2020)