I have run into this a few times working on Chevy & GMC trucks. It's one of two things IMO, the multifunction switch, or the brake light switch. I think I would try to remove the brake light switch and look at it. Possibly try to replace it. If it doesn't work, just return the part. I had one test good on an S10 & it drove me nuts, turned out to be the brake switch.
I've also ran into the multifunction switch causing the same issue, but I'd try the brake switch first, easier and cheaper to replace. I have no diagrams, sorry. Please post when you figure it out.