It's easy to see the fog lamp wiring if you remove both the back cover and the fog lamp cover. A visual inspection should tell you if the wiring is going bad. Check for brittle or cracked insulation and all wire/connector joints.
My guess is that it's a bad connection at the headlight socket, though. Check and clean both socket connectors with contact cleaner and make sure that the car side of the socket is firmly in place.
Headlight side of the connector and pin layout...
Here you can see that the fog light and turn signal wiring do run close together as they pass by the main reflector. If the wiring is bad, it would be simple to run new wires by removing only the rear and fog lamp covers.
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