Blowing ignition fuse

Absolutely. Fuses often blow for no reason when reconnecting the battery due to the momentary current surge from memory circuits charging up.

There's a good chance your brake light switch is just loose or out of adjustment. It only takes a minute to check it. That would be better than driving with your brake lights on all the time. The switch is under the steering column, and the white button in the photo gets pushed in by the brake pedal's arm to turn it off. Two nuts on the threaded shaft hold it tight and are for the adjustment.