Fog Lamps Dont Work On 03' Toyota Corolla

You need to perform diagnostics to verify where the problem lies.
Possible causes are :

1. Fog fuse.
2. Fog relay.
3. Front fog switch.
4. Wireharness.

Unplug the fog relay and test terminal # 1 & 5 for battery voltage. If voltage is not present, check fog fuse for battrry voltage.

Use a fuse jumper, bridge terminal # 3 and 1 or 5 and if fog light comes on, check the fog switch.

How would I go about checking to see if the fog lamp switch on the left control arm works or not?

Unplug switch wireharness and turn fog lights on. Use DVOM to test continuity between terminal #2 and #4. continuity should exist and when switch is turned off, there should be none.

Alternatively you can use a test lamp to ground the Red/Yellow wire to test the relay circuit. Do not unplug wireharness, backprobe the terminals taking care not to damage the terminals. If light comes on, turn switch on and backprobe the Orange/Green wire. If light comes on, switch is good and you have a fault with the DRL control unit or there is an open withe Orange/Green wire to DRL unit.

Awsome! Thank you very much for the assistance! I'll let you know how it goes!

You're welcome.

Have a nice day.