go to a motorists' or yachties' accessory shop and buy some "Jenolite" (clear liquid acid rust remover) in a small plastic bottle.
Don't buy Kurust or Navy Gel or any other rust remover.
Using rubber gloves and eye protection (it burns) put a little on a paper towel and rub it on the rust stain. It will probably disppear in a minute. if not, you can leave a bit of paper towel, wet with jenolite, lying on the stain and it will soak in (it also works on glazed china plates, which you might expect to be impervious)
Rinse off several times with water.
I don't know if it will affect the gloss, I've never noticed a prob.
Don't put it on stainless steel as it will stain it.
Coca-cola also works as it is slightly acid, but will take far longer.
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