I have a 2001 Silverado 3500 2 wheel drive dually. I put a flat bed on it and when I tried to hook the lights up to standard 6 way lights on the flatbed the turn signals turn off when I apply the brakes. Now I have a trailer and the problem is carrying back to there. I hooked up a separate set of lights just for the turn signals and that worked but it is still carrying back to the trailer. I never had this problem until I switched the bed.can anyone please help?

 

bad grounds can cause this.

on the oem lights; were the brake and signals separate bulbs?

 

I had the same issue when towing a small utility trailer. As mentioned above, ended up having a bad ground.

It was fun trying to master "turn signal, cancel turn signal, then brake/turn" for a trip.

Look at each spot there is a ground make sure it's really clean, good contact, solid mount, then try weather-proofing somehow (paint/dielectric grease etc).

good luck