im not sure if it has anything to do with the battery not being there. but blowing bulbs is usually because the regulator that controls the voltage coming out of the lighting coil is kaput or not there. if you can get your hands on a multimeter you could measure what voltage your getting to the light. with the key thing i have heard before that its a position just for running the light and the engine isnt meant to run when its in that position so i wouldnt worry too much about that.
will
85 Tri-Z "Rumble Bee"
85 250R "Red Rocket"
83 200X "Flat Tracker"