With the bulb in, check for continuity through the circuit by using a test light or multimeter on the headlight connector pins. One of your test light or multimeter leads should be on the turn signal positive pin and the other should be on the common ground pin.
If you have a good continuity between the turn signal positive pin and the common ground pin, remove the bulb and test for continuity again. If you have continuity with the bulb out, there is a short somewhere in the circuit.
You can also check for continuity between the rear connector pin and the socket itself. These test will determine if you have a break in a wire somewhere inside the headlight OR a short-circuit caused by brittle and cracked insulation which is very common.
If the headlight checks out, report back.
