Finally had time, cooperative weather, and the vehicle at home so I could have a look at this issue. Sure enough, one of the overhead console mounting screws were laying in the panel and dropped into my lap when I popped the panel off to have a look. When I re-secured that screw, I figured I'd tighten the other one, just in case. It, too, was loose!
I'm thinking that these things probably never get tightened well enough during assembly because there's no straight shot to the screws with a screwdriver. Hopefully, we won't have to do that again, but I now know how, if we do.
To get to everything, you have to first pull the console cover off. That's the panel where you garage for control (if so equipped) maybe OnStar, and as was on our PPV, the console light switch. To get this off, I dropped the sunglasses holder down so I could get to the back of that panel with a plastic pry bar. There's a clip on either side of the light switch, or garage door opener buttons, depending on options. Pop those loose, close the sunglasses holder and then pull down on the back of the panel until it pops loose.
The screws secure the overhead console to the body, and are kind of hidden, being black and going into a piece of black plastic. In the pictures, I have put a circle of white marker paint on one of the screws, so you can see where it is when installed. In the pictures where you can see the marked screw, the back of the truck is to the left.
I hope this helps someone. It's certainly odd to discover the source of the sound you're CERTAIN is in the dash.
