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

You wouldn't be the first to find fault in the backside of the fuse box. Those females aren't locked, boxes get water in them from leaks, etc...
Your dimming park lamps and dimmer rheostat varying park lamps is my focus. That just shouldn't happen if everything gets 12 volts through solid connections.
If bulkhead, fusible link, ALT' gauge was the culprit, every dang thing would suffer low voltage, more circuits turned on would take away from other circuits.
Current will take the best path or path of least resistance to ground. The path through the wiring and elements in headlight bulbs is a lot better than through those smaller wires and bulbs.
That still suggests low voltage/amperage everywhere. Are you testing with battery only or with active charging system or both ? Do results change?