Start and Ignition Problems on 71 Demon

You could try applying 12 V from the battery directly to coil+. Use a jumper wire of 16 awg or larger and good alligator clips (or a ring terminal). If it runs well then, the problem is erratic wiring from the ballast to the coil, or the ballast itself. You need a timing light to see if it is firing at the right time (when it does fire). Used ones are real cheap since not used on newer cars.