Had a go at this myself. I didn't realise but the standard item is either anodized or painted. I think there's 2 reasons for that, 1) reduce reflections in the cockpit, 2) ensure it doesn't tarnish with hand grease/sweat etc (ugh).
Anyway I went into this thinking a quick bit of autosol polish would fix it, but eventually I was using a Sisal mop with polish soap stuff. Some of the paint/anodizing wouldn't shift so I used 400 grit, 800 grit then 1200 grit then the polish.
Came up nice in the end, worth a couple of hours in garage.