Most likely high resistance connection. Use a meter to check for 12 volt at connector with bulb removed, ignition on and brake pedal pressed. Alternatively, with ignition off, remove bulb and use a small, sharp screwdriver to scrape the bulb holder connection and the tip of the bulb; replace and try again. The fact that the high level bulb is working indicates that the circuitry up to the rear of the vehicle is probably ok. Hope this helps, it worked for me.
Andy