I went through a lot of this when I was installing different switches from stock in my new dash. I checked for voltage at the terminals on the headlight and dash dimmer switch with the connector only plugged about 3/4 in when I was trying to figure out the wiring for my new (cough cough) Chevy billet headlight switch (I wanted 1 switch for everything instead of 2). IIRC there is only 1 large wire (pink I think) that goes to the headlight switch. It was pretty easy to trace the wires by checking voltage on all the terminals then moving the switch to park and checking voltage again etc...

Your issue with the front parking lights is almost exactly like what I mentioned in my post above. The housing itself has to be grounded if it's the same as my 72 (only two hot wires going to light connector, 1 for park, 1 for turn signal). I used a test light and actually checked the bulb contacts in the socket to test for power.

I'm wondering if you might have more than 1 problem. Even though these issues appear related, I have been guilty of looking for 1 big common problem when it really was a couple of little ones!

Good luck with it!