Intermittent No start.

There's always a KIA ^^^^ (know it all) . . . . . didn't sound like a bad switch issue to me. It sounded like a ballast/module issue to me. I know I'll get hammered for this,the Chrysler electronic ignition system is ancient technology with to many pieces. To add to that , most replacement parts are poorly made parts made in other countries. the ignitor system is simple,and it works. :lol:

Here's the deal man.
The factory ignition system has two circuits that come out of the ignition switch.
Ign.1 and Ign.2.
When you turn the key to the on position you are supplying the ignition coil power through one circuit. (the run circuit)
When you turn the key to start, the ignition is supplied power through a different circuit inside the switch. (the start circuit)
If you crank the engine and it doesn't fire until you let off the key it means the start circuit isn't getting power but the run circuit is. (usually)
A low battery can also cause this because the coil doesn't get good power until the starter isn't cranking but the engine hasn't quite stopped turning yet.

Sometimes it's caused by the "Start" side of the ballast being burned out and only supplying power to the ignition through the "Run" circuit. (let the key back from start and suddenly there is power to the coil and the engine tries)
Other times it can be a wiring issue, and others it can be the ignition switch or wiring in between.
And THEN there's the random spark from the coil every time you turn the ignition off from the coil field dropping, so that can also confuse things a bit when there's a pop from a cylinder when the key is turn off when the engine hasn't started after being cranked.

So, only firing when the keys is let off the start position usually means the power to the "Run" side of the ignition is dead for whatever reason.
A different ignition module type would also not have power to it in the "Run" position.
PLUS, the point made above about replacing parts with parts that can usually only be ordered is a totally valid concern.

IMO, you are a bit new to be calling people you don't know anything about "Know it all".

I also vote for a bad switch, connector or wiring to the ballast. (since he replaced the ballast already)
It's also possible the pigtail connector on the distributor is making an intermittent contact because of the heat cycling of the engine.
(Turn the key off from cranking, the coil field drops and POP)