I had the same issue on a 01 suburban we used to have where the tow/haul would work intermittently, I got my 00 silverado and the switch worked fine for awhile, then got sketchy, would only work in certain gear selections (3rd vs D, etc) and while we were putting in remote start and were there anyhow we found the famous orange wrapped wires had completely busted.

Soldered it back together and the truck is ready for summer hauling the boat back and forth to the lake...

Hope this helps those with the issue. Not a hard fix, just got to take the trim off the bottom of the dash/column and it's right there.