Turn and Brake light on TT only work on one side

The OP said the tail lights work but turn and brake don't. Turn and brake are the same thing (same filament). It may simply be a burned out bulb. Change the bulb or connect the trailer wiring to another vehicle to see if it works.

If a new bulb still doesn't work even with a different vehicle, the next place I would check is the trailer plug connections. Pull the housing back and make sure all the wires are still connected and tight.

Depending on your vehicle, in the "old days" when one bulb when out on the circuit, everything went out on that circuit. We'd start tracking it down by checking the fuse, the look at each bulb that uses that fuse. And every time, one was blown. I had one car that when the brake light bulb blew, the radio quit working too. Another one, when one of the bulbs blew, the dash lights went off too.

So, not knowing how your vehicle is wired, I'd double check this idea first.

Another thing, more than likely your trailer tail light uses the 1157 bulb, which has 2 filaments in it. If both are out, it's probably the ground. I had a utility trailer once that drove me insane because one side kept going out completely. No brake, no turn flash, no running light, all 1157 bulb. Every time, it was a broken ground to that bulb socket, which was actually in plastic and had a separate wire connected to the trailer frame.

I would check that second.

I would check the ground connection. Do you have a volt meter for 12 volts? Use a volt meter and run a ground wire to the battery to see if you have voltage at the 7 way connector and at the brake light assembly.

Time for the DVM Digital Volt Meter. Check at the truck connection end and at the brake light end. While someone has their foot on the brake. You can find the wiring diagram here:

Pinout

This will localize the problem to the truck or the trailer.