Ignition backlighting 69 Swinger.

Time delay relay is likely bad. It Is a thermal device by design. The longer the yellow door switch wires are grounded ( i.e. Door open) the hotter it gets and the longer the key switch is illuminated! It was used into the 2000 plus model years and readily available. Any Mopar with A01 option had them. It looks similar to a flasher but smaller and longer. If you see yellow wire or wires and a pink going to it you found the right piece. Like Cosgig said these cars with the A01 option use dual contact door switch's. The second leg though is used for the headlight on buzzer feature and is likely yellow with black tracer. Look around the ashtray to locate it.

My 69 Barracuda has it and it works just fine after opening and tweaking it a bit! I did not realize just how available they are so I decided to tweak mine into submission. Napa probably even sells them!