Learjets are called C-20s in the Navy. USN also flies 737s, DC9s, and a few P-3A's for transport purposes. With the exception of the P-3s, all of these jobs are piloted by either reservists or TAR personnel. The reservists are guys from other fleet platforms who applied for and were accepted into those units for their reserve commitment. Each reserve squadron has something like 6 TAR officers as well. Since a reserve unit isnt manned full-time by all of its personnel, the TAR (Training and Administration of Reserves) folks are full time with the squadron. They are similar to active duty, but are considered part of the reserve component.
Bottom line, don't even think about flying something non-tactical until AFTER your initial contract is up and you've done your time with the warfighting fleet. Those platforms aren't even an option as a selection choice after primary.