Engine stalls once starter is released.

Whenever you have spark ignition with an individual ignition coil, there is always a resistor in series with it somewhere. That makes it run on an average of around 9 volts. 10 - 11 volts is what the battery voltage will get drawn down to during cranking, and the ignition system must be able to operate with that voltage. When you add that lower battery voltage and that resistor, the combination makes the coil run at around 6 - 7 volts. That would produce a very weak spark or none at all. To prevent that from causing a hard start or a no-start condition, that resistor is always bypassed during cranking.

It's the resistor circuit that has a break in it causing the no-run condition. The break is being bypassed when you're cranking the engine. That's why it runs until you release the switch. Failure of that resistor was real common on some cars in the late '70s and early '80s, and the symptom was exactly as you described. With yours, however, since it occurred right after sitting a while, I'd suspect a corroded connection that plugs into the resistor, or a mouse chewed on a wire.

I'm sorry I don't know how your resistor is bypassed during cranking. Chrysler did it with a separate contact built into the ignition switch. That provided full battery voltage to the coil. GM did it with an "R" (resistor) terminal on the starter solenoid. Ford also did it on many of their models with a second small terminal on their starter solenoid that sat on the fender. I imagine someone could have done that with a separate relay too, but I don't that for a fact.