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A little more info on the truck will help with the diagnosis. If its a Torqshift, behind the 6.0 PSD it is a Tow/Haul button, 7.3 would have O/D switch.
the harness in the column can get chaffed and cause problems with the T/H switch.. There are a few screws to be removed from underneath to remove the trim and you can inspect..
Mine is having the same problem But the actual button broke off the end before I bought the truck. It would still work when the end of the button was broken and when a I found the broken piece i glued it on. At that point the tow haul stopped working, I think I need to buy a new lever with button...