The fog light relay is in the underhood fuse block. You can see it in the diagram on page 6-74 of the 03 owner's manual, (a PDF of which can be downloaded from viewtopic.php?t=755
) its the one right next to the FOG fuse
Power for the fog lights comes from the battery, goes through the 100A ALT fuse, then through the FOG fuse, then the fog relay to the fog lights. The relay is switched by a combination of the fog light switch and the daytime running light module.
If there was a problem with the battery or the 100A ALT fuse, you would be worrying about a lot more than just the fogs.
The fog lights only come on when the headlights are in full low beam mode. They will not light when in half bright DRL mode, and will not light when headlights are high beam. The fogs do come on if you manually turn the headlights to full low beam, and turn on the fog light switch. Don't need the car to be running, don't need a key to check that.
One thing to check to determine which half of the circuit is problematic is to pull the relay and use a wire, or a paper clip to jumper the connections in the relay socket. When you pull the relay, there will be two probably silver colored tabs , those are for the relay coil, and two likely copper colored tabs. When the switches and DRL module put 12V across the silver colored tabs, the relay will close and connect then two copper colored tabs. If you jumper where those two copper colored tabs go, you can turn the fog lights on and completely bypass any control from the switch and DRL module. Let me know if that doesn't make sense, and I'll get around to finding a picture, but not tonight
If you jumper that and the fogs come on, then the problem is probably in either the switch or the DRL module. If it doesn't come on, then the problem is in the bulbs, the FOG fuse, or something with the light socket or wiring itself.
The fog relay is similar to others in there, you can swap two and see if the prblem follows the relay or stays with the fogs