BJ is right. Brass is an alloy made from copper and zinc. Joe, Brasso is abrasive with quartz or silicon. Brasso Gadget is abrasive free but I have never used it.
Careful with Brasso. It works great on hard brass but is very harsh and can scratch things up in a hurry. It is hard to tell the thickness of the plating on that fixture from the photos.
I have always liked Flitz for metals I was not sure about. You can get it online or even at auto parts or marine parts places and I suppose hardware stores. A tube of the stuff will last you a long time.
Your real lighting store will have probably have safe metal polishes. Most janitorial supply places sell retail now but you end up having to buy more than I suspect you want of anything.
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