Check to see if water is getting into the brake light sockets causing them to short to ground
A blown fuse is always a sign of excessive current flow. In this case, it's probably caused by a short circuit in the brake light wiring.
The trailer has a dead short in that right side brake light circuit.
Tail light assembly short
A short in the brake light circuit.
A short, water getting in the light socket. exc.
You probably have an electrical short somewhere in the line.
There is probably a short in the wiring.
Well you narrowed it down to an electrical problem, get yourself a dmm and start chasing wires.I've also seen a bulb burn out and short causing the fuse to blow when the brake pedal is depressed. double check your fuse again and if its still good have at it with the digital multimeter.
The 1997 Pontiac brake light fuse is located in the fuse box. The brake light fuse will be labeled as the tail light fuse.
Check the circuitry to the backup lights. The same fused circuit is probably used for both brake lights and backup lights. As you go past Reverse, the backup light probably is turned on briefly, causing the fuse to blow. It's just a thought, but I'd think it worth checking.
the third brake light is direct from brake light switch no fuse