I had this problem, but only with the ABS lights coming on. Same symptoms where it would go away if you restart the car.
I instrumented LEDs and volt meters to the ABS module in several places and found that if the circuit to the ABS bulb in the instrument panel is broken for any amount of time, 22seconds later, the ABS warning signal would enable and stay on until it was reset by turning the vehicle off.
I removed the instrument panel and found the intermittant circuit to be a bad solder joint on the cable socket. This could be the case for your ABS as well as the brake light circuit. | 
