Brake lights not working

Yes, that would probably indicate a problem with the brake light switch. As for how to take that clip off, just stick a decent sized flat head screwdriver in the "U" end of the clip and turn it a bit to spread the "U" and then, while still keeping the screwdriver turned, slide the clip off. It may take a few tries, and is unnecessarily annoying, but it will come off. The images below decently illustrate what you are dealing with.

Also, here is a decent YouTube video on the subject: https://www.youtube.com/watch?v=iv2D_nm8Jck

And another one: https://www.youtube.com/watch?v=K8k5gSXAlJc

Please let us know how it goes for you.

Thank you. The video you provided was better than the one I found, still same principal though. Yes it is unnecessarily hard! If I can just get that clip off the rest should be relatively easy provided that is the problem. :)
Note for other readers: the hazard lights also work with no problem, it is just the brake lights but all three. Since all three do not work I do not believe it is the multi function switch (turn signal).

My thoughts as well with respect to the turn signal switch.

I would like to inform everyone that it was indeed the "Stoplight Switch" as it is called by AutoZone. However, take special care with that retaining clip as in the process of putting it back on it had flipped off on me rattled around and disappeared. So now I am on a mission to find a replacement.

Yep they can travel when removed. Use 2CarPros anytime, we are here to help. Please tell a friend.

Cheers, Ken

Yeah, I should've warned you about that possibility. Sorry about that. But at least you got to the root of the problem. As for finding a replacement, AutoZone should have one on the shelf in a small set of retaining clips for GM's. Thanks for using 2CarPros. Come back anytime and bring your friends too.