Use a test light and connect one lead to a solid ground, something other than the ground wire of the tail light. Turn on the brake or turn light and touch the test light to the power connector. Does the test light illuminate? If so, the problem is with the ground to the light fixture. If the test light doesn't light, the problem is on the power side.
Larry, Eileen, and Finley
2004 Alpine 36FDDS
Third motor home, first Alpine, no need for another.