Here's a fun one...

1971 Imperial with an early 90s era Mopar electronic ignition retrofit kit. Yes, the old orange box that still works.

The car has been performing beautifully. It fired up at the first twist of the key. I drove it about 20 minutes and the car didn't want to restart. Now, it will only start when I release the key. Or, if I put the key in the run position and jump the solenoid.

Yes, the single row ballast resistor is good. 1.5 ohm as designed, otherwise it would die when I released the key.

I removed the starter solenoid wire to reduce voltage draw. Testing wires at the ballast resistor I get 12.3 volts at the brown (start) wire with the key in start. No voltage with key in run. Blue (run) wire shows 11 volts in run and nothing in start. A bit low but it functions fine.

I pulled the bulkhead connector and cleaned the already pretty clean terminals on both sides.

No change.

Ignition switch is good.
Wiring is good.
Terminals are good.
Battery is good (a week old).

Why won't it start properly with the key?

You are checking V at the ballast output terminal, have you checked V at the coil? Seems like that 12.3V isn't getting to the coil. Possibly a bad crimp?
Could try a jumper to the coil
Also verify the module is getting 12V as I've had a few that were wired to the wrong side of the ballast
Next check your grounds and possibly even run a ground wire from the block to the module
keep us posted

Voltage at the coil is good, otherwise it wouldn't run. Ignition 2 (start) bypasses the resistor and shoots voltage to the coil. Ignition 1 (run) goes through the ballast resistor, down the same connection used by Ignition 2, and to the coil. If the coil lead was faulty the lower voltage from the ballast resistor wouldn't make the engine run.

Grounds have got to be good because the engine runs.

System is wired properly because I've been driving the car all over town. The Ignition 2 issue just popped up. The car still runs, you just have to hope it catches on key release or jump the solenoid.

I did not ohm out the ign 2 wire between the ballast and coil. It's the same piece of wire that runs the coil on lower voltage from ign 1. The engine runs so that section of wire is good.

if all wiring and voltages check out ok replace the magnetic pickup...i have twice had the problem you described and the pickup cured it.

Not talking about that wire. Talking about the one from the ignition switch to the coil side of the ballast. In start, what is the voltage at the coil? If it's not there work your way back till you find it, ultimately it comes out of the ignition switch.

It may very well be a case of your starter loading down the system so much there is not enough juice for the coil to work, but once you release the key the voltage goes up enough to fire the coil.

Voltage at the coil is good, otherwise it wouldn't run. Ignition 2 (start) bypasses the resistor and shoots voltage to the coil. Ignition 1 (run) goes through the ballast resistor, down the same connection used by Ignition 2, and to the coil. If the coil lead was faulty the lower voltage from the ballast resistor wouldn't make the engine run.

Grounds have got to be good because the engine runs.

System is wired properly because I've been driving the car all over town. The Ignition 2 issue just popped up. The car still runs, you just have to hope it catches on key release or jump the solenoid.

as Annaroseannadanna [not sure of the spelling - an old SNL character] always said : "it's ALWAYS something............."

Sounds like you have multiple problems going on. Or perhaps, just one really bad ground connection somewhere.