My guess is button. Looks like the setting is intended to keep that stone in place through some rough movement. The facets look good in the one picture. My guess light green Topaz. Is it sterling? If it is than I would definitely point to a semi precious gem. Its a round cut but its hard to tell with the setting. If it is a button it could have come from a ladies cashmere jacket. That's how I can imagine it at least.
I found a ring and the setting for the stone was a full wrap around like yours(no points)perhaps that type of setting was particularly to an era .Could narrow your search.(button)