I've done this twice in the last couple of years. I only have before and after pictures of one of them, and I will try to take pictures of the other tomorrow.
The first one I did was an Agile AL-2000, Honey sunburst flame. The thing looked
like plastic. I stuck a plastic steel wool substitute to a random orbital sander, and hit all of the gloss. After that step, it was pretty dull. I then brought it up to the shine I wanted. I used some rubbing compound and a drill-mounted polishing pad to remove some of the scratches, then rubbing compound by hand, and then carnauba cleaner wax a few times. It left the instrument with a nice, warm sheen, and I think it looks a lot better. Pics tomorrow.
The second one is my Squier Cyclone. I did this one entirely by hand. I used the plastic wool, and then rubbing compound, and then cleaner wax. I like the results.
Before:
After: