Welcome to the forum!
If by "mirror finish" you mean Nickel Plating, there isn't much you can do for it, other than to have it re-plated, which will be a bit expensive for a few spots of rust.
If you mean "stainless steel", then I've heard Mother's Mag or Flitz Polish and some elbow grease will get the job done. Possibly steel wool?
Finally, if you mean it has a polished-blued finish, I've also heard a light steel wool (0000) and some oil should get the red-rust out and leave the bluing.
In any case, I'd say just to give the gun a very light coat of oil to protect the finish and prevent any more (red) rust from appearing.