Hook up to positive on the battery and look for ground at the unit.
The ground wire to the module in particular.
Coil getting power doesn't mean the module is getting 'Grounded'...
Since it works when you ground to the battery and turn the shaft, the trigger is working, and the module will work with sufficient 'Ground' connection,
So it has to be something with the 'Ground' when it's in the engine...
Where are all the 'Electrical Experts' that like to argue every point when you need them?
They like to argue every little point I print, the HEI fan boys argue every ignition thread, especially when I suggest you avoid HEI 'Clones', but they disappear when someone has an issue!
Since I've had similar issues many times in the past having worked on these things for over 40 years,
I can't say I have a definitive answer for you,
But where I would start looking...
I've often recommended using a LONGER SCREW at the 'Ground' terminal on the module (The one with the metal connector where the screw goes through),
By using a longer screw, and if you can find one, use a BRASS screw,
And attach a 'Ground' wire to the screw where it sticks out the bottom of the housing.
Use a brass Nut or two to hold your dedicated, serviceable 'Ground' wire in place with direct connection to the module.
Since the coil grounds through the module, giving the module a dedicated 'Ground' will make the entire system work more efficiently.
'Ground' has always been an issue with HEI since the aluminum housing gets surface corrosion, and aluminum oxide is a LOUSY conductor...
This is SIMPLE, quick, doesn't take $100 to do and makes the system work closer to it's 'Optimum' potential.
I've said it over and over again,
Rust in the distributor hole, oil residue, corrosion on the housing, ect. all conspire to keep your ignition from working at it's optimum,
And basic electrical principal says if you get electrical 'Juice' into the ignition module/coil, you MUST have a good path for that current to get back to the negative of the battery for the unit to work at it's full potential.
There is something going on here,
Since the unit WORKS when you have dedicated 'Grounds',
And you have power to the module 'Battery' terminal AND the coil,
It stands to reason the unit isn't getting 'Ground' (Negative Path to complete the circuit)
You are getting a little education here,
Think about the guys that plug along for YEARS with partial 'Ground' not even knowing the ignition is barely working!
Not a clue about the 'Potential' they never realized... Didn't even know was there!
I would add a DEDICATED ground to the distributor housing, as close to the 'Ground' terminal on the module as possible,
And see what happens...
This won't cost you anything but a longer screw & a couple of nuts, and maybe a minute of drilling to insert that longer screw since it's an odd ball thread...
Since you have a nut on the bottom of the housing, threads aren't required anymore in that hole,
And you have a dedicated grounding post for your dedicated ground wire.
If it fires up and starts working with a dedicated 'Ground' then you have solved the mystery.
If it doesn't, you haven't lost anything, and gained a good 'Ground' for when you DO find the issue...
The dedicated 'Ground' doesn't work,
Have a LONG HARD LOOK at the wires from the 'B' and 'C' terminals on the module to the coil.
That would be the 'Pig Tail' that plugs into the cap.
'B' terminal should have power up to the coil, which you have checked.
I dont know if you checked the wire pig tail, or actually lifted the dust cover and checked for connection at the coil terminal in the cap, but make sure you are getting full battery power at that terminal in the cap.
'C' terminal is the 'Green' wire to the coil. This is the 'Ground' connection for the coil.
Look for corrosion at the module to harness connector, and I don't know if you have the 'Unit', plastic plug with 'Condenser' attached to it,
Or you have just a two wire plug type.
Pull that connector off the module, and the cap, check the WIRE for malfunction, corrosion, ect.
If that wire is making good connection at both the module and coil terminals, then you should be OK...
That would put you back to NOT having a solid 'Ground' to the module or housing.
The Screw that 'Grounds' the module is next to the 'C' terminal...
Once you have VERIFIED the connections and KNOW things are getting power inside the unit, then you have eliminated everything but 'Ground' to the unit...