The EASIEST solution is to pick either the right brake light/turn signal or the left brake light/turn signal and hook to that. It will function perfectly fine as a brake light, but will flash with that turn signal. By tapping into both the right and the left signals, you don't get increased functionality as a brake light, but you get flashing on both turn signals AND backfeeding, as you have found.
The harder solution is to find the wire feeding your third brake light and tap in to that.
photobug wrote:
Got one controlling the 3rd brake light on the coach. it's too big to fit on the bike rack, and don't want to mess up the hitch wiring if I need to tow something.
After posting, I saw you posted this just before me. This gives you the perfect answer.
Tap into the "STOP" wire and "GROUND" wire and run them to the light bar with a
2 pin connector rather than the trailer hitch connector.
Bobbo and Lin
2017 F-150 XLT 4x4 SuperCab w/Max Tow Package 3.5l EcoBoost V6
2017 Airstream Flying Cloud 23FB