Hei conversion Intermittent start?

Easiest to remove the distributor so you can spin it by hand, instead of cranking the engine and running down your battery. I would ground the body of the distributor while doing this, just in case it matters (would w/ points). You need a good way to view the spark when testing. Trying to fire the whole engine is too "whole hog". Chew on an ear first, i.e. getting reliable spark. If you don't have the $4 Harbor Freight in-line lamp, arrange a spark plug with a grounded jumper wire to the electrode or body. You could do the old trick of "place plug tip near engine metal". HEI should throw a 1" spark in air, but your plug end could slip, cause over-voltage and maybe fry the module. I recall from the earliest days of HEI, warnings to never run it with a plug wire off (like doing the old trick "pull each plug to see which cylinder isn't contributing"). Be careful because it can shock the bejesus out of you.

Things I see:

1. Run a dedicated ground wire under a mounting screw (as others say) and insure it touches the clean metal rivet on the HEI module. Run it direct to BATT- first, until it sparks reliably.

2. I don't see twisted wires for your 2 distributor pickup wires. Indeed, yours appear far apart, making a big loop, known in EE world as "an antenna". You don't want pickup from anything but the VR sensor inside the distributor.

3. Your HEI module looks like the $12 Chinese one. I prefer factory parts from the junkyard and keep a new ebay cheapie as a spare.

4. That coil will probably work. Check that it isn't getting too hot. I hot-wired 12 V direct to a factory coil to drive my 64 Valiant home after purchase and after 5 minutes it started missing bad above 40 mph, with points. The coil was almost smoking. Jumpered in the ballast and ran fine then. The HEI better controls dwell to not waste energy in the coil, but works best with an E-core coil, which you show in later photos, though the wiring is suspect there.

5. If starting from scratch, I would suggest a junkyard 8-pin HEI module and matching "external coil" (85-95 GM trucks, 93- cars) since one also grabs the cable that links the two for a very simple hookup. I probably paid $15 both times I grabbed a set (plus slipped in the knock sensor and module). TrailBeast sells those parts new for $99. Hard to beat the new $45 HEI distributor on ebay, especially if one doesn't have an electronic distributor. Did you read the reviews here (search "ready-to-run" or "HEI")?