2002 Chevy Avalanche the tow/haul switch

No, there is no fuse on this circuit. I have seen this problem before on chevy trucks. On the trucks I saw this problem with I found the wire broken near the shifter. Remove the bezel around the steering column. Check the wire coming out of the shifter. Usually breaks a couple inches back from the from the shifter. Even if the wire does not look broken, it could be broken inside the installation. Check if the wire is stretchy. If it is, you know it is broken inside. If it is broken you will have to either repair the wire or replace the entire shifter. If it isn't, it could be a bad switch. Good luck.