Rear signal lights out, bulbs good

My car has auto lighting. When I have engine off, but radio on, the tail lights are on. When I turn the engine on, the tail lights are still on. When I press down the brake pedal, braking lights are off. Braking lights are always off. I.e. regardless engine on/off, headlights on/off, braking lights are off. I suspect that the taillights are out when I am driving b/c people give me the high-beam signal at night lately and it is always dark behind me when there is no other cars behind me.

Thanks a million.