Frank I had that problem with my blinkers. There are a couple of causes. First is LED tail lights. If they are installed without a load resistor, this can happen. Try driving with your headlights turned off, when I had that problem, it only happened with headlights on.

The other is a bad ground on trailer wiring. Try disconneting any wiring for a trailer comig from your tail lights.

Basically your turn signal is grounding through your brake lights. If you watch closely at night, I bet you can see your tail lights flicker with the turn signal when all your lights are turned off