Need help with brake lite problem 66 barracudaa

I have a 66 barracuda, just restored, 1 brake lite on, use the turning switch, then the left goes out and the right comes on, back and forth, put in used switch, same problem, then we bought a new unit, same problem, had car painted, with lite units out, could it be a bad ground? If you take the lever, for turn signals, and go up and down just a little each way, both brake lites will come on, turning signals work good, as running lites. Any body have had this problem , and how did you fix,??!! 66bcuda in il.