That is kinda cool problem. I would look at the ignition switch too.
Was this a modified harness for HEI? Take the power line to the coil and measure it to ground, with and without the lights on and see if it a full 12volts or just a partial. In any case you should have no voltage on that line.
I still think you should run this test of pulling the positive wire off the coil and testing for full +12 volts with lights on/off. If you don't have voltage on the line, I would be more inclined to agree that its a grounding issue. If you do have full or partial voltage on the + side wire of the coil start chasing it back.
If you have the yellow line on the coil that is an easy check to pull that off and see if that is playing a role. I wouldn't think it is as it has nothing to do with the light switch. But check it anyway.
Then your down to just tracing out the pink wire under the dash. Your main red power comes into the car feeding the light switch, ignition and fuse box. The ignition feeds the pink wire that goes out to the coil but is also shared by the Gauges, reverse lights and a few other things.
As for the Amp meter its a stand alone gauge that doesn't have a ground reference that I recall. Just two 12volt sources from different locations that would cause a small trickle of current. I still need to trace that my self.
