If I explain the circuit, you should be able to figure it out yourself. The headlight switch supplies power to the control side of the fog light relay. The switch supplies the ground path to the relay. The power side is fused.
To get into the wiring you need the factory Electrical Wiring Diagram from Toyota, aka EWD.
You will need to check power, ground, to a switch and a relay. And check the operation of the switch and relay.
My first guess would actually be two bad bulbs. The lights are on the lowest part of the car, and pick up debris easier down there.