I had this problem once.. It was due to a faulty brake light bulb. It was a 2 filament type - where one is for the rear parking light and one is for the brakes. There was a short in the bulb.. (The bulb may not be the one in the center lamp either. Check them all.)
Does the center light work when you press the brakes (if the lights are off)? Do the front parking lights turn on when you step on the brake pedal?