Alright, this isn't making any sense to me. I followed the picture write-up, with the exception that the foglight relay wire that's being rewired was red/yellow, and the foglights are working LIKE NORMAL.
I spliced together the red/green fog light wire to the black/white wire, capping off the dashboard end of the red/green and leaving the black and white at a complete circuit. Even though the foglight relay no longer clicks, the fog lights come on... ONLY when the headlights are on driving beams! I also hit it with a test light just to make sure I wasn't seeing things, and sure enough, it only lit when the fog switch was on and the driving beams were on.
What the fuck!?