I'm in agreement with 180, I would look at the relay or Brake switch first as the cause.

It would help to have a second pair of eyes monitoring the Brake lights, as you play in this area.

If it was an intermittant short, it would depend where in the wiring circuit it was occuring.

If it was a short between the power source and switch, I think you'd get a BAS or Light out indicator, without touching the Brake Pedal.

If the short was where it picks up the ground to light the lights, you'd need the pedal depressed.

I guess what I'm saying is if you eliminate the Fuse, Relay, and Brake switch, and suspect the wiring (a short), you'd need to look carefully at the wiring diagam and the symptoms, this will help to narrow where the issue might be.

An intermittant short might not necessarily blow the fuse, it may just complete the circuit, and light the Brake lights (falsely)...