If you can take the red lens off and look carefully at the bulb. When you have the turn/brake on you should be on the thick filament. What you might see is the thick filament is very faintly lit, and the thin filament is brighter.
Very often what happens is you see a flashing/brake indication through the red cover, but it is actually lighting the thin filament. If you find that to be the case, the problem is the ground connection to that bulb socket.
You can check that by bringing your negative from your battery to the bulb socket, and touching it to the bulb socket side. If the lights work properly then you have found your problem.
On re-edit... I presume you know that the brake/turn signal to the trailer is fused, and that you may have actually blown the individual side fuse that feeds the trailer brake/turn lights, one for each side.
