As an hobby car detailer I use the following process when doing an older car when I am not sure of the paint condition regarding the clear coat.
If you are patient and want to carefully and slowly bring back some luster to your paint, try Maguires Cleaner Wax with an orbital polisher (not a buffer) ie. Like Porter Cable with an initial Green finishing pad then a final Black polishing pad.
The Cleaner Wax is a very gentle product and unless you are completely reckless you won't burn through the clear coat.
It will be a slow multistep (but rewarding) process to bring the luster back.
Don't be afraid of using a lot of the product on the pad initially, which might seem messy, and go slow with the orbital speed for the first couple of polishing sessions.
You can apply some pressure at this juncture, as the extra compound will help lubricate the pad and protect the finish. I did my Mom's old Black Lincoln in this manner as I was concerned with the thickness of the clear coat.
It was a boat and I had at least 24 man hours invested. Outcome was extraordinary.
Later when using the Black polishing pad the apply like 5 large drops of Cleaner Wax on the pad and do a finish polish. You can go faster with the orbital speed, but don't press on the polisher. The weight of the polisher will do the work. Don't let the pad dry out.
I would practice these steps below the shadow line of the doors and rear bumper to get a feel for the process. Cleaner Wax is inexpensive and has always been my go to product for the final polish sequence on older paint.
If you just happen to be anywhere near Joliet Illinois, I have a heated garage and all the stuff. We could knock this out in an afternoon.
Good Luck.
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