It's too darn late tonight to think clearly, but I think you have a problem in the bulkhead/ ammeter/ underdash in harness splice."

I believe that a wiring fault has disconnected the battery from the alternator feed so that the lights are drawing power from the alternator, but the alternator is not connected to the battery. Check carefully in that area

If that splice has broken loose in the harness, it's possible that part of the conductors are connected to the alternator feed, and part of them are connected to the battery

For example, my '70 book shows that the black wire from the ammeter AND the feeder for the headlight switch both terminate at that splice. I'd be considering untaping the black ammeter wire until you find that splice

I posted this out of my 67 manual because it's pdf



If you find the ammeter to the far right, note "R6A-12BK" at the bottom of the alternator and trace it back, where all that stuff comes together is a big splice "in harness."

Now notice that L1-16-BK takes off to the lower right of the splice, and runs right down to the headlight switch. THIS IS the main feed that runs the lights.

If somehow, that splice came apart in such a way that some of the car was "being fed" power and other parts were not, this could explain what's goin' on.

(In my lifetime, I've found three cars that had one of those spliced fail. First one, I remember, was a buddies 68 Roadrunner--the ammeter would dance all over hell. We were sitting in the car in a driving rainstorm, the harness and dash all over our laps. I found it and fixed it, and he just could not believe it.)