2011 4.8 2wd tow haul?

[James1994]

New to the forums! I recently bought a 2011 silverado 1500 with a 4.8. The truck is a 2 wheel drive and has a 4l60 transmission. The problem I have is when I click the tow haul button it doesn’t kick out of overdrive nor does it hold shifts longer leading me to believe it doesn’t work. I’ve read about most of the problems with the wire running to the button inside the shifter coming loose and not allowing the tow haul light to come on but my light comes on when I press the button. Any ideas or is the truck not equipped with tow haul??