I love to search for cufflinks in antique stores. Some stores have drawers full of cufflinks to look through. I've seen this type button in those drawers, but never in a pair and most have a polished stone agate like yours. I never looked in to what they are, but just assumed them to be a single button for those old stiff collars. Some I've seen have wonerful looking high polished moss agate and banded jasper stones in them. I have never found any to be of solid gold or silver, as that is what I'm looking for along with signed popular makers in these drawers full of cufflinks. Very cool little find.