MASS metal polish as a last resort, but start with a rouge cloth for polishing sterling silver . Wrap it around some small objects to get into small places.
Turtle Wax Chrome polish.
Top it off with a few coats of McGuires #26 Yellow wax and then New Finish on top of that. Wax will shine it, New Finish will protect the wax. That`s what goes on my black car and it looks unbelievable.
Last three items are from the auto supply store.
A tooth brush will help clean the deep grooves.