I drew a diagram. Not sure it is simple enough, though. You have a replacement wiring harness? I guess it is a single fog lamp, not a pair of lamps.
To be able to turn on the fog lamp at all times, connect an always hot wire into one of the aux switch terminals. (You probably have an always hot wire going into something on your aux panel). Connect the other aux switch terminal to relay terminal 86.
Connect relay terminal 85 to ground. Those two connections are what will energize the relay coil, generate the magnetic field, and move the internal switch, thereby connecting terminal 30 to 87.
Run a circuit from the battery (or a connection point that is wired directly to the battery - I am assuming no ammeter is in use here....) to a (new) fuse and then from the fuse to relay terminal 30.
Connect relay terminal 87 to the lamp's positive terminal. Ground the lamp's negative terminal.
Lamp is 48 watts. That is 4 amps at 12 volts. I'm thinking a 10 amp fuse is appropriate, though not 100% certain about that. I think you'd be too close to tripping a 5 amp fuse. Others will likely chime in on that fuse amperage rating.
You'll want at least 18 gauge wire from the battery to the fuse and from the fuse to the lamp. 18 gauge wire can handle 10 amps for 10 feet. Bump up to 16 gauge if your run will be longer. 16 gauge can handle 10 amps for 25 feet.
If you don't connect directly to the battery with a new wire, which I don't expect you will, i.e. you tap into some existing connector / connection point, then make sure the wire that goes from your connection point back to the battery is heavy enough to handle the additional 4 amps of current. It should be a beefy cable, like the thick cable that connects from the battery to the starter solenoid on a stock series V harness or the cable that connects the starter solenoid to the fuse block. You don't want to be adding more current load to a small 16 or 18 gauge wire.
Mike
