MRose,
I was just about to start a new thread because of this same problem. Like I posted earlier I installed 2 harnesses, one in my 96 1500 and one in my 01 3500. The setup in the 1500 works great and I think it is because the Pilot fog light setup is different than the stock setup.
This morning was the 1st opportunity to use the headlights & fog lights in the 3500. Previously I just tested the hi and low beams. I am getting the same symptoms. As you noticed, your hi beams are on with the fogs. I believe the reason is that the normal fog relay ground path is thru the high beam filament. With the new harness, the ground path is thru the relay causing it to activate and turning on the hi beams. That's my theory but I don't have my wiring schematics handy to check it out. I will try to pull the fog relay later to see what happens.
ON EDIT> Well, I just went out and pulled the fog relay to see what would happen. As expected, the fog lites did not come on and so the hi beams did not come on. All other light operation is normal. Reinstalled the relay and checked again. This time the fogs and hi beams worked as normal. Hmmmm. This is with the truck off so I surmised that the lower battery voltage was not enough to trigger the hi beam relay. I fired up the truck and sure enough, the hi beams are on with the fogs. I just need to figure out what to do for a remedy. I am thinking a resistor inline with the hi beam relay but will have to figure out a value to use. The best bet would be to remove the fog relay ground circuit from its current path. Will have to wait till I see the schematics.