Found this today. Posted on facebook and was told it's a wax seal by a very knowledgeable person. Absolutely beautiful and blessed to find it. Thanks for looking, Chris
Yes usually stone, the cutting is actually called intaglio, which is technically engraved, not cut, and it's engraved onto a Chalcedony stone (from the quartz family).
I found a nice gold plated cuff link with an Orange Chalcedony stone that had a similar greco-roman intaglio bust engraved on it. You frequently see these on rings of the late 1800's.
