I'd suspect the trailer ground wire is not making a good connection at the frame. This could result in your brakes and marker lights getting a ground through the trailer ball. When you apply the brakes the trailer weight pushes against the ball making a good connection. When you release the brake the ball and hitch may loosen enough to make the lights flash.
A friends TT did the same thing as yours. His marker lights would also go on and off while driving down the road. He spent 2 days trying to figure it out. I stopped by to help him and found two problems.
1) There was rust on the bolt threads and wire connector where it contacts the frame.
2) the painted frame itself did not make good connection and only relied on the bolt for a ground.
We removed the bolt holding the wire to the frame, used a grinder to clean off the paint, replaced the ground wire eyelet connector then applied some neversieze to the bolt thread and reattached. Then spray painted any visible bare spots.
Check the ground wire first.
Oops, I just saw you posted this in 5th wheel but the problem may still be where the ground wire connects to the trailer frame.
