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I just got a 1990 C4 painted in "Root Beer Brown". Unfortunately, it has a couple spots on it where the paint is peeling. What is the best way to touch up these spots? Here's a picture of where it chipped around the rear tail light:
Is that something that's doable without previous experience doing bodywork?
Anything is do-able with the knowledge and with the right materials and equipment. Sorry that it is peeling on you already. Most likely it will continue on other parts of your car. It is a sign of bad prep work.
There are several ways to do it. With no experience, I would suggest getting some touch up paint made up. CAREFULLY scuff the edges with 400 grit paper to remove loose paint and feather the edges, and then dab on the paint to cover and fill the spots. This will take several applications. Once you have the spots covered and filled, CAREFULLY sand the area with 800 and then 2000 grit paper (available at automotive paint stores). Then polish the areas with rubbing compound. This appears to be a MAACO or similar paint job, notice the flatness of the paint and the scratches, other than caused by collision, so I wouldn't suggest a re spray, because it requires a lot experience to do it right.