Not knowing what you did/ changed for wiring, I can't say specifically, but here's how it "used" to work.

Chrysler ignition switches have THREE important, separate circuits inside, that is what amounts to three separate switches SO FAR AS THE ENGINE goes.

1. Ignition run. This is normally the blue wire, which feeds the ballast resistor (originally) the regulator, electric choke if you have it, and the alternator field on 70/ later cars, and may feed the idle stop solenoid, don't remember. In any case it is LIVE in "run."

2 "Engine start." This is the wire that feeds the fender/ firewall mount start relay, and fires up that relay when you twist the key to "start."

3 Ignition resistor/ ballast "bypass" circuit. This wire ALSO comes from the switch, and feeds "hot" battery to the coil + when the key is in "start" and is normally brown.

I would guess that you are missing this last connection. You have a wireing diagram?