Check the splice in the 4x4" metal box in the A-frame (near battery) for the turn signal wire. Also check the ground connection there. Connections/splices can be poorly done and/or corroded. When you find the correct wires and the copper isn't a bright color, you should clean the wire (stranded) with a wire brush, or better, with a chemical cleaner.
In our TT, the turn signals are connected with a 2-wire cable (ground & positive) continuous from the turn lights to the 4x4 metal box in the A-frame that connects to the wiring harness from the 7-pin connector and requires a good ground as well as a positive. You could test the turn signal lights by taking a piece of wire and jumper 12 volts from the battery to the 7-pin connector. If no turn signal on, you could try the same thing at the splice in the 4x4 box and if you can't get the turn signal to come on, would suggest a break in the wiring between A-frame and turn signal, but would be the last thing to suspect.
Could also be a bad ground connection inside the 4x4 box. There will be a larger splice of a number of white ground wires (5 or 6?) and black in the wiring harness and the connection could possibly be faulty there. Only other thing might be corrosion at the turn signal? Remove lamp and verify 12 volts at the light.
While in there checking things out, I'd suggest inspecting the other connections and splices. They are exposed to the elements and subject to corrosion plus the factory may not have done a good job to start with.