Unfortunately we'll probably never know; but here are a few lines of inquiry that remain open to us.
1. We can work to gather evidence of every John Miers ring known to exist.
2. We can attempt to trace the whole history of the ring from manufacture to museum.
3. We can compile a record of cameo rings from that period thought to be of Epicurus.
There is a "Sherlock Holmes" element in all of this that pleases me immensely—the game is afoot!