I experienced a similar problem with a 1931 Coupe I restored for a friend. The car had previously been "restored" by a "professional", but my friend said he could never be sure he'd make it home after a drive. It didn't run right on the road, he said. After rebuilding the entire car - including the ignition system - a test drive showed that sure enough - the engine missed upon acceleration or at a sustained speed. I checked out everything and found nothing wrong. Backtracking, I decided to disconnect electrical items until I had isolated the troublemaker. By sheer dumb luck, the first item I disconnected was the oil pressure gauge light wire that ran to the terminal box or ammeter, I don't recall which. (An auxiliary gauge was mounted at the bottom of the instrument panel.) A test drive proved that the light in the oil pressure gauge was causing the engine to misfire under power demands.
So, I can see why turning on something as equally harmless as a defective instrument light could play havoc with the ignition system. Try completely disconnecting the wire first and see if that makes a difference. If it does, then do as "mcgarrett" suggests and connect it to the ammeter terminal closer to the speedometer, the usual place for this wire (on a 6 volt system). If the ignition cuts out again, then you know for sure there is a short inside the instrument light, probably a frayed wired where it exits the light's body.
Marshall