You don't normally have any sort of control module on the trailer. Some tow vehicles have relays that separate the trailer circuits from the car circuits but most just connect directly to the car circuits.
If you have any sort of test equipment the best thing to do is isolate if the problem is in the car or the trailer.
I like working with a test light, which is a device that looks a lot like an ice pick with a clear handle and a wire coming out the back. You connect the clip on the wire to a good source of ground and then probe with the pointy end. These cost less then $10 and are available at most auto parts stores and many hardware stores.
To test, clip the wire to a good metal part (chrome or unpainted) of the hitch, bumper or frame. Take the test light and probe the contacts of the light connector. Find tail lights, left turn and right turn. Note that BRAKES use both the left turn and right turn so if you have turn signals you should have brakes.
If you don't get anything at the connector then the problem is in the car. If you have a vehicle with a factory installed tow package, such as what came on a Ford Expedition or similar, then you may have a set of relays for the trailer. My Expedition has a fuse box under the hood for this feature. It is interesting to note that these fuses are NOT mentioned anywhere in the owner's manual!
If the lights work at the connector then the problem is in the trailer. Check the lights themselves and make sure that they are not full of water. Check the wires all the way back. I have had situations on really poor ramps where the trailer tires fell into a hole, which made the frame hit the ground and crushed the wires underneath.