Wiring gremlins
First do you have a legitimate FACTORY service manual, either paper or CD or BOTH? Nothing less will do
Second, take each problem "one at a time." Now there ARE weird things that can happen and cause strange backfeed problems
For example, one member on here (might have been OldManMopar) told of when they were kids, they found out they could listen to the radio with no key!!
I don't remember exactly, but I think you turned on the 4X flasher, stepped on the brake, and maybe flipped the signal lever one way or the other. In any case, "all this" caused a backfeed condition which allowed the radio to work -- as long as your foot was on the brake!!
I don't know how much different the 71 harness might be. You can download SOME manuals for free here:
http://www.forabodiesonly.com/mopar/showthread.php?t=132309&highlight=manual,+download
About the first thing I'd do is string the harness out, take an audible (if possible) continuity checker, or a light, and find out which bulkhead terminal each and every wire hooks to.
IF this is a complete harness, there's a couple of wires that do not go to the bulkhead, IE the green field connector for the alternator (push on) goes up to the regulator plug and nowhere else. If you have the electronic ignition harness intact, one wire from the ECU goes to coil neg (eyelet)
Running your park lights off the ignition is a REAL bad idea, as the ignition line is ALREADY somewhat loaded, and is NOT fused.
Post back here and we'll try'n walk you through
Photos here and there might help, too.