Refinish Black Plastic Fore Stock & Pistol Grip Caps On Winchester 70

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I have this rifle I bought new in 1974 that is dang near mint. I'd like to get it as close to "like new" as I can. The fore stock & the pistol grip both have decorative black caps trimmed with a white spacer...looks nice. But the clear coat has come off these two caps a bit. Anyone with any ideas on what I should do to repair these? I'm thinking about seeing if I can just scrape or sand the remaining clear coat off. Then would I be better off to spray on a clear finish or maybe just polish it with something like Fletz BPO3511 Metal, Plastic, and Fiberglass Polish.

 

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Scraped off the clear coat on the ebony end caps, sanded with grits 220 - 2500 & polished with polishing compound. Looks great! Took maybe a couple of hours. Could have used Flitz, maybe, but really didn't need it.