It's frustratingly difficult trying to diagnose someone's wiring diagram remotely. You really need to be there, meter in hand.
I agree with Barry (BlackJota) that the switches aren't the problem if taking them out of the circuit completely makes no difference.
Your photos only tell part of the story. It's difficult to tell which is the live feed from the battery to the fuse box, and we can't see the cables that connect to the brake light itself, so it's not clear where the brake light is getting its power from. There's normally a live feed from the battery and a switched feed from the ignition switch that go to the fuse box, but we can't see which is which.
I'd guess that fat red wire connected to the bottom of fuse#1 is from the battery. Or maybe the battery feed is to the top of that fuse. It's unclear, but it may be a reasonable assumption that fuse #1 has a live 12V feed. That would imply that fuse #2 is switched by the ignition key switch.
The wire labelled "red wire from rear light switch" is connected to the same point as the other big red wire, so presumably that's the 12V supply to the live side of the rear switch. We can't see a power supply to the front switch, but I guess it must be somewhere.
The two cables you've labelled "switch wires" that join together at the bottom of fuse #3 are presumably the switched power return from the front and rear switches. What else can they be? The top connection at fuse #3 has a jumper across to fuse #4. That would imply that the wire connected to the bottom of fuse #4 goes to the brake light. If so, then the power to the brake light is going through 2, maybe 3 fuses! That's a bit convoluted but it could still work.
The thing I'm suspicious of is that other black wire connected to the top of fuse#3 that disappears off to the left of the top photo. If it connects to a 12V supply somewhere (fuse #2 that is switched by the ignition switch perhaps?) then it'll power up the brake light independently of the brake switches. If that's indeed the case, then it makes sense of your test result of disconnecting the brake light switches and the light staying on.
Disconnect the left wire from the top of fuse #3 and see what happens. I suspect that wire shouldn't be there.