You might try using your cell phone camera to take a picture, It can see what you can not
There are basically three bases used,,, now one of these is highly unlikely,
Screw in (like a regular 120 volt house lamp but smaller) You already said you think that's not it, and it is very rare in this type of service
Bayonet Push, turn pull
Wedge.. Just pull
(And pin another Just pull
use of an inspection mirror (My lady's compact perhaps) or your cell phone camera might get you a better view of the base and a clue.