Unless your trailer has separate lights for brake and turn then if you have a left turn signal, but not a left brake light, then the problem has to be in the tow vehicle.
As Chris said, check the fuses in the tow vehicle. Get the manual out and read it carefully. My Ford Expedition, as an example, has two separate fuse boxes. A box under the dash has all the common fuses for the car. A second fuse box under the hood has the really large fuses and all the trailer wiring fuses.
If your tow vehicle happens to be a type that has separate turn and brake lights then I would guess that the problem is in a relay somewhere that converts the three light system (tail, brake & turn) to the two light trailer configuration. That relay would probably be in with the fuses.