How to clean

I have this gold plated Waltham I bought as a present for the Mrs. The rear cover needs a bit of a clean/polish at the edge. Any recommendations of how to go about this without going straight through the plating would be much appreciated.

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I’ve used a polish called Flitz and had good results. Didn’t seem to take off any noticeable amount of finish. 

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I'd say a jeweler's rouge cloth. Supposedly a Cape Cod would work too, but I have no experience with those. Brasso is probably too aggressive.