Electrical nightmare, 1968 cluster lights, parking lights, horn, etc.

Does it add up? Headlight switch has 2 power supplies to it, B1 and B2. B1 shouldn't take power away from B2 unless there isn't enough power to begin with. Illumination dimmer shouldn't take away from/effect park lamps either unless B2 is suffering low voltage.
So lets go back to the trunk of the tree... A big black wire leaves the ALT gauge. Then it has a factory weld splice where branches go to various places ( so no splices isn't exactly true ) .
One branch goes to headlight switch B1. Another goes to the fuse box to power a buss bar where the hot at all times circuits are supplied. I believe there is a voltage drop in this somewhere.
There is also a branch to the ignition switch. With ign' switch on this feeds a wire to another buss bar in the fuse box. Turn signals, blower, wipers, and more are here. If none of these circuits suffer low voltage, thats good. I suppose I would drop the fuse box, pic the back cover off and have a good look at both sides. Just crusty fuse clips can cause voltage drop.
Since you mentioned the inst' panel... there are 2 connectors with a orange wire in each. 2 illumination bulbs per wire. This is where we get "only 1 half of my panel is lighted" threads. I don't read that you have that problem. I don't read blowing fuses either.
I have to ask though... About that round panel connector, have any of those female terminals been out of it? Another owner once read the factory diagram wrong, put the wires in the wrong positions and had all kind of screwed up electrical. Why their engineer decided to rotate this connector 90 degrees on paper is still a mystery to me. Regardless the orientation on paper, the locating key in the center dictates wire positions ( it was drawn correctly ). That owner needed only to move his beer and rotate his drawing 90 degrees LOL
last 2 paragraphs are probably TMI Get factory wiring diagrams, study B2 Good luck