"I assumed George H. W. Bush had signed up to be a fighter pilot but became a bomber pilot and George W. had elided that transition."
You didn't sign up to be a fighter pilot.
You sign up to be a Naval aviator cadet. If you made it through all of the preliminary testing, education, and training, you graduated with the rank of Ensign and went on to preliminary flight school.
It wasn't until you hit advanced flight training that you were ASSIGNED, based on everything that came before, as well as your performance in advanced flight training, to be either a single engine (figher, torpedo bomber, or dive bomber) or multi-engine pilot.
Probably every kid who signed up for the Army Air Corps or the Navy had visions of being a fighter pilot, but no one walked in, said "I'm signing up to fly the F4F!" and actually got that without going through the training program.