Brake lights go out when head lights are on. During day brake lights work fine. At night when driving with lights on, applying the brakes turns off the rear tail lights. The center brake light in the rear window is not affected. When you take foot off brakes rear tail lights come back on.

What most likely you have on the rear lights is a bad ground between the lights and the frame /chassis. If the lights are on a tailgate /hatch then the wire is probably broken in the space between the 2 units where it moves a lot. Try running a temporary spare long wire between a known good ground on the frame and the grounding side of the lamp to see if this is fixes the problem or not. Turn on the emergency flashers to simulate the brake light action (that way you wont need two people to test it). Then you would obviuosly have to find a way to shorten that connection and make it permanent.

Most likely a bad earth to the light's. Re-earth the tail lights should sort the problem.