[A1971Blazer]

blown fuse indicates a dead short in the circuit....the brown wire going to the rear harness is the running (tail) lights...NOT the brake lights.....at the rear cross member there is a connector for the rear light harness...unplug it and try the new fuse again...

if it doesn't blow again then the short is in the taillight harness...if it does then the short is before the connector/harness....either way you will need to trace the wire to find where it's shorted...