Check your engine to body ground at the rear the ground usyall goes to the heater fan mounting nut.
The wire going to the starter relay to the bottom forward prong is the ground for the relay. 69 and earlier are permantly grounded on standard shift cars. 70 and newer it goes to the clutch pedal. All automatic cars the wire goes from the three prong or single prong trans switch to the starter relay.
It would have to be that the car is grounding the incoming ballast wire.. or positive coil. This wire is blue and is the same wire that operates the Alternator,electric choke, AC , and Ballast resister . You are shorting the this wire when the lights are on. This will prevent them from working. These are just some guesses. Without seeing the cars wiring these suggestions are just something to check. I believe you have something plugged in at the wrong location. Go get bulbs at NAPA. I have had problems with chain store bulbs they are so loose they go in the wrong way and short the system. Take the bulbs out and try it.
While the car is running unplug things and see if the lights still keep shutting the car off. unplug all the blue wires under the hood except the ballast. One at a time. something is shorting that wire or the brown wire coming from the ballast to the coil.
This would be just a guess but is this car 74-79? I pulled my hair out on several of these years losing spark . Including trucks and vans. It was always a ground shorted to Positive. Never walk away from this car or truck with the battery terminals on. They light on fire real quick.
