Electrical problems can be a bear to sort-out. I've done a lot of automotive wiring over the years & seen some interesting problems. Some the result of bad practice, some the result of failures, grounds rotting off, etc.
Reading what you've written, a few things come to mind:
Changing your wheel & adding a tach means you've had to touch the wiring. I changed the column in mine & had issue with one of the turn signals because one of the pins on the column wiring connector popped out of position. Point being, you should verify the integrity of any the connection points you've touched.
Grounding is another issue that can result in weird symptoms. Absence of a ground in the right place means that the circuit will try to find another path. I had a headlight ground that rotted off one time & every time I put the turn signal on that side, my headlight & turn signal would alternate off/on because the ground was trying to go through the headlight filament to get to that ground. If memory serves; there is supposed to be a ground on the column. Did that get re-installed? If it is hanging loose & it makes contact when you hammer the brake while the car is moving the wire may be dangling around, but when the car is still it isn't... Something silly like that.
Is the tach wiring correct/working properly? Where is that ground connected?
Lastly (& I've seen catastrophic results of this one)... Nothing will burn a car down faster than an electrical fire. Its effectively a cascading failure. Once a circuit pulls enough current to melt the insulation, that wire melts into other wires, shorting them out & so on... The only thing to do at that point is pull the cable off the battery, or let'er go & call the insurance. You said your horn button was shorting/overheating. That's bundled-in with your column wiring, which is in close proximity to the brake wiring... It's possible you have an intermittent short. The other thing I've seen happen is the wiring insulation gets very brittle with age - especially if it's seen a lot of current & when you handle it, insulation breaks away/falls off leaving bare spots... Another possible issue for short circuits.
I know it's tough to get in there - not a lot of room (I'm 6'-4" & 260lbs)... but I would get a good light in there & check all connections & verify grounds, follow the brake circuit wiring. Having a wiring diagram & volt/ohm will also help.