Are you sure it is the turn signal lights and not the running lights? If you have a short in your trailer wiring between the left signal and the running lights it might backfeed the truck through the trailer connector. I would think the truck lights would be sort of dim on the right side.
If the right and left turn signals were shorted then I think both right and left would light all the lights.
Check over your trailer carefully for a spot where the wires are pinched. Also take out the left turn bulb on the trailer. The short could be inside the bulb if the filaments are touching.