Unfortunately this won't be extremely helpfull, but sounds like a short. Is there a lot of moisture in the air on the days when this happens.
I had a similar problem in another vehicle. On damp days, like really humid, or it just rained or something, the ignition wouldn't work. Turned out water was getting in the wiring.
Best idea I have is start with the brake pedal, there should be a sensor connected to it, and start looking for corrosion in or around connections, and keep following the wires. Not sure where the wires could cross with the other lights as I am new to jeeps, but it's a start.