I suspect a wire is grounding out on something else. I'd literally trace the wiring from the turn signal light to the turn signal switch and carefully check for any problems with the wiring along the entire route, looking for wires that might be rubbing on something or otherwise open. I would also check the electrical panel that folds down under the dash and holds the circuit breakers and some fuses and look for anything on the panel tray that might be causing wiring interference. Loose connections, frayed wiring, etc.