A moon shuttle conductor was an individual who was in charge of a moon shuttle.
In 2155, in the mirror universe, Commander Jonathan Archer hallucinated his prime universe counterpart taunting his aspiration for remaining captain of the USS Defiant. The illusory Archer claimed that if Admiral Black had his way, "if you're lucky, you'll end up commanding a moon shuttle!" (ENT: "In a Mirror, Darkly, Part II")
In 2266, aboard the USS Enterprise, Doctor Leonard McCoy was berated by Captain James T. Kirk for not alerting the captain on the ship's red alert status during a physical. The doctor then quipped, "What am I, a doctor or a moon shuttle conductor?" (TOS: "The Corbomite Maneuver")