You could use your DMM to measure the AC voltage directly across the bulb socket. If the bulb is rated for 120VAC, the transformer specs shouldn't matter.
I like to use 120VAC led bulbs that are made for type 47 (BA9S bayonet, also called T1-3/4)) sockets, like these:
http://www.superbrightleds.com/moreinfo ... e-angle/3/
Make sure the bulb is rated for 120 AC volts like the ones I linked to.
Another consideration is that the socket you used might not be rated for 120VAC. The typical Fender style, like it looks like you've used, isn't. These are:
http://www.elightbulbs.com/Sylvania-321 ... Light-Bulb
With your setup, it may be easier to just switch to the heater wires and use a 6.3V lamp. I like to use 120VAC lamps because I can run the pilot lamp right off the Power switch, and avoid running extra wires back and forth from the rear to the front of the chassis:
[img

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http://i514.photobucket.com/albums/t346 ... wiring.jpg[/img]