HEI ignition troubles

What I'd do:

1....De-wire the system and "hot wire" it to eliminate all car wiring possible problems. In other words connect a jumper to coil+/ HEI module and jumper direct to battery

2...Double triple check that module is actually grounded. To do that connect your jumper power and stick your voltmeter on a good ground, like the block or battery NEG post. Stick the other terminal on the module mounting holes metal grommets. There should be ZERO reading.

3...Suspect the distributor connector. Those can be problematic as there is no real power there, so a slight amount of corrosion can stop the "works. "Work" the connector in/ out several times to scrub the terminals. Since you have access to the HEI module, connect your meter to the pickup terminals at the HEI with meter on low AC volts. Spin the dist or crank engine. Pickup coil should generate about 1V AC