you could getcha a 6 volt wall wart, A.C. or D.C. dont matter. unplug pin, unplug all jones plugs in back box, and put the wires from the wart across any GI bulb, and see if they light.
This is an easy way to test bulb runs,and a short touch to the bulbs, will usually not kill the wart. "most are protected from that".
The divide and conquer method may be good too. you can cut the braid and mend pretty easy.
and, yes, you can put led's in the bulb sockets. though they may tremble so much, it bothers your eyes. can always put the bulbs back.