[esox07]

So, are the left turn signal and brake light working on the truck when the trailer is plugged in? If the truck blinkers and tail lights work with the trailer plugged in, then go back to the trailer lights and check them for power at the light sockets. If you are getting power there, then it is the bulbs. If not, move up and check just before the wires enter the lights. If no power there, then move up to the front of the trailer and check the wiring there just before the plug. Then check before the plug. Once you finally find power along the system, you know the problem is between that point and back to the previous place you checked. It is just a matter of narrowing down further between those two points.
Keep in mind the trailer (Or Truck) could have had some customized trailer wiring done to it at some point.