cleaning up cruddy geared tuners

How would you suggest cleaning up nice geared tuners that were stored for so long a bit of crud has accumulated on the surface? 

I recently acquired a dulcimer that was stored in its case for probably a couple of decades.  It has nice gold Grover tuners, but a bit of crud subverts their shine. Are there specific products that would work?  My wife has some stuff she uses to polish jewelry.  Should I just use that?