I use Tarn-X all the time to clean my base metal jewelry (if I
haven’t oxidized/patinated it). A quick dip (1-2 seconds) and a fast
rinse & dry does the trick. When followed by a few quick rubs with
the silver polishing cloth, the brilliance is back! Tarn-X contained
acidified thiourea (whatever that is), and sometimes it smells like
rotten eggs, but I can put up with that, compared to the time and
mess of using something like Brasso.
I put the Tarn-X into one of those dipper bottles, and you can use
the same small batch over and over again. No need to throw it out
after one use, although you may want to make up different dipper
bottles for dipping different metals. For slightly larger items,
handy dipper containers are those Tupperware pickle holders, which
show up at a lot of garage sales.
The Tarn-X bottle says not to dip (among other things) “pearls and
other stones.” Things like agate do not seem to be bothered at all
by Tarn-X. I have a large lapis cab, in a brass setting, which I
have dipped (occasionally and rapidly) for years, and it doesn’t seem
to have damaged the stone. It may look a little dull, but oiling it
(with, e.g., hand lotion) brings back the sheen to the lapis, which
never had a high sheen in the first place.
I can’t make any guarantees, but these are just my experiences.