Welcome to TreasureNet Todd!
Is the inside of the hole on the back threaded by any chance? And does it seem intact, or possibly broken off? So far I'm just trying to determine if it's indeed a button, rather than perhaps a decorative medallion that might have been affixed to something, similar to what old wooden hand saws had on their handles.
Under super-magnification, I can see that it is definitely not a button. In addition to having such a prominently raised rim around the back (which buttons don't have), the attachment at the back's center is not any of the forms used on buttons. In my opinion, Nhbenz is on the right track, some sort of metal stud or rod fit into the raised circle on the object's back.