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.

OP edited to specify no aftermarket splices. I'll dig around the switch a bit, test for power there, and trace those wires out according to the diagram.

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.

The fuses for the turn signals, blower, wipers, etc are all at 11.7-12.2V - The only one not in that range is the instrument cluster, which is around 6V.

I cleaned all of the fuse clips a few weeks ago and replaced all the fuses with new ones.

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.

Correct, neither side illuminates, both orange wires have power.

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

I have no idea if they have been removed from the clock or not over the last 49 years (I sure haven't pulled them out), but I will double-check that the orange wire does line up with the pin to illuminate the cluster.