Towing brake lights

When we hook the car up to to the caravan then test the lights the brake lights come on then go straight off and will not work at all on either the car or caravan, yet the indicators still work. If we remove the brake bulb on the O/S rear light of the car it will work but obviously not the brake light on the car where the bulb was removed. Changed the bulb holder still no difference. We know problem is with the car as it will work on a different tow vehicle. There is no problem with the lights when we tow our trailer, just the caravan? Please help!