They will run on low voltage. In fact they do. The ballast resistor lowers the voltage to the coil and the 5 pin ecu. They won't start on low voltage though. That's why they have a separate start circuit. Anyway... The fusible link and bulkhead is a good place to start looking for your voltage drop. If all good there, check the ignition switch connector under the column.
If you had about 12 feet of good wire you could temporary a route around, run it from battery positive to that ign' switch connector ( largest black wire there ). If it fires right up the fault is somewhere between the engine bay side and that connector which includes the ALT' gauge. We saw picks of one of those gauges melted down a just few days ago, and it was in a 73 model dash.
This fault would lower voltage to everything except the starter. Headlights, etc.., would work just not as good as they should. So maybe the first check would be, What else is operating on less than 12 volts? If everything except ignition is getting good current, the ignition switch and the blue with white tracer through the bulkhead is suspect. They added a choke heater to all the stuff already pulling through this wire. We've seen this wire connection melted recently also.
By the way, the ballast resistor shouldn't get kinda hot. It should get very hot. That's why its ceramic encased.