Hell, when all else fails, blame the ground!
I've been known to do this
I have never changed any of the wires and they are configured as they came with the car.
Maybe you personally didn't, but Randy's ideas makes good sense.
I would first unplug the 3-wire FOG switch and try it out to see if the FOG lights come on that way. If the problem went away, I would probably next check the 3-wire connector for the Fog light switch (harness side) and find the 12v+ power with the headlights and/or running lights on, and after finding the correct pin, turn OFF the headlight switch and provide a 12V+ jumper into that pin. THE HEADLIGHTS SHOULD NOT COME ON, but instead, only the taillights. If the front PARK lights also come on, this too is incorrect. If it works as it should with these tests, just your switch or that Bad Ground.
If the problem DID NOT go away by unplugging the FOG switch, you might wish to check your grounds (that sounds better than asking you to check your shorts
)
Hopefully, that should narrow down the playing field a bit.
Richard