I'm glad this was brought back up so I gave it another look.
I found something for 1982...is it the same as 83/84? I would guess so, but I'm not a Buick guy, so I don't know. Interestingly for Monte Carlo, it only goes to 1982 on the listing as well. WTF?
GM p/n 557325. And they are square mounts with a round face, if that makes any sense. Lemme see if I can dig out my little box of these somewhere and take a picture. They are for the bezels on Oldsmobiles, but they're discontinued and I don't think they're made by anyone aftermarket. I don't have many, so I can't let any of them go, but at least it may give you an idea what they look like.
Previous GM p/n was 412219. Was used in a lot of various cars, A,B, C, D, G, and X bodies from 1976 on up through late 80s for sure.
Here's the pics. It APPEARS this may be what you need..of course, drywall anchors may work too. I think that's sort of the principal method these things work off of anyway. Pop them in, then when the screw runs through it, it expands 2 expandable tabs on the sides to make it larger and squeeze up tight.
🙂