My one experience with an HEI module dying was I went to a gas station to get a soda, truck was running fine, park, shut it off, come back and go to restart and nothing. Replaced module (in the parking lot) and all was well again.
Is the vacuum advance hooked up? I had the wires for the pickup get fatigued and under certain conditions with the vacuum advance moving it would start missing/cutting out. If I kept a super light foot it would be ok, but try to give it any more throttle vacuum would drop and begin cutting out. Also check the connections at the cap, both the connector from the base of the distributor, and the terminals in the cap. I’ve had them either get pushed up into the cap and make poor/bad connection or the female terminals in the pigtail fall out of the connector body and make poor connection.
I’ve come to find that I should never discount or write off any possibilities with this type of stuff. Numerous times the problem was something I wouldn’t have believed had I not dealt with it myself. One of my favorites (to tell now that’s dealt with) was after I did a dingle ball rebuild on the slant six in my Dart. Get it back in and running, had some issues with intake and exhaust leaks, got those sorted, I had noticed that when it was hot the vacuum gauge would bounce like crazy, when it was cold it was steady or at rpm’s off idle it would steady out. Readjust the valves a few times (solid lifters), keep checking for intake leaks, carb adjustments, etc. Finally worked my way to thinking valve springs, sure enough I could open a valve with one finger, while running I could push lightly and make it hang open, or pull up carefully and vacuum was steady again.
Replaced them with “340” replacement springs and low and behold, the issue went away for good. There was a few contributing factors to this, one is I had the head cut for compression and a valve job, which would raise the valves height, lowering spring pressure, I reused the stock springs which ones used in production were weaker than what was ever offered as a replacement (replacement springs are the same as 318 springs) from Chrysler or aftermarket, and I did put a slightly bigger cam in it. So yeah, valve float at 700rpm
