Taylor served aboard Enterprise for three years, presumably from its launch in 2151 until her death in 2154. Prior to this, she served on the Saratoga. Commander Tucker pulled her off to be on Enterprise, making Captain Brody angry. She was considered a gifted engineer, and was particularly adept at repairing fused power relays (especially those which Tucker was unable to isolate himself).
Taylor was one of eighteen crewmembers (affectionately referred to by Captain Jonathan Archer as "The 18") killed during the Xindi attack in the Azati Prime system in February of 2154. The section she was in (identified as either section 6 or 7 of C deck) decompressed while she was heading to her station; she died right outside her quarters. It was said that, had she made it "a few more meters," she would have survived the attack.
Taylor served on Michael Rostov's engineering team, and he frequently played practical jokes on her. Tucker maintained that one day Taylor would make a fine chief engineer; she once found a glitch in the injector assembly that everyone else missed.
Upon Taylor's death at the hands of the Xindi, Commander Tucker was ordered (over his objections) by Captain Archer to compose a personal letter to her parents. Trip had difficulty writing the message and, after at least two false starts, successfully did so only after speaking with Taylor in a dream. The process was emotionally trying but therapeutic for Tucker, ultimately resulting in his coming to terms with the earlier loss of his sister Elizabeth.
Taylor kept a framed photograph (apparently of herself and her parents, though this is unclear) on her desk in her quarters. It was damaged during the Xindi attack in which she was killed. (ENT: "The Forgotten")
The full text of Commander Tucker's letter to Jane Taylor's parents follows:
Mr. and Mrs. Taylor: By the time you get this, Starfleet will have already told you about Jane. Since I worked so closely with her, I wanted to add my personal condolences. I have to confess, I've been putting off writing this for a while. I convinced myself that my duties on Enterprise took precedence. But the truth is, I didn't want to face the fact that someone so young, with so much promise, could just be gone. But I'm facing it now. And I found myself thinking how important she was to me. She was a great engineer. And she was my friend. She won't be forgotten.
Her rank was somewhat unclear. Like her fellow engineer Rostov, she was referred to in dialog as "crewman" (an enlisted grade), although her uniform rank pips were those of a lieutenant. This may be attributed to a simple oversight on the part of the production team (similar to what happened with Miles O'Brien on TNG), although there are other indicators that Taylor could have held officer rank: