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I just installed my lights on Sunday. When I cut off the PIAA switch, there was a thin black wire and a white wire. I spliced the white wire to the purple wire under fuse #39 and ran the black wire to ground. The large white wire on the PIAA harness went to the aux battery post (next to the fuse block) and the large black wire was grounded next to the hood strut. I don't remember any red wire(s)...
Hmmm. It's raining heavy right now; I'll try to look at mine in a while when it let's up and see that red wire. I'm sure others will jump in and offer their expertise...
Here you go, bro. Take a look at this electrical diagram.
As you can see, the thick black wire with the ring goes to the ground. The thick white wire with the ring goes to your battery +12V connection.
The thin white wire is the relay wire. This is the one you need to hook up to the purple wire under the fuse #39. (And if you have the stock fogs, it's easier to splice into the stock fog wiring harness)
Let me know if there is anything else I can do to help.