The ball and post style shown in the OP seems to be a later improvement of the standard riveted finial that was in use at least back before the US Civil War. Those were secured similar to the common rivet and burr. In other words, the acorn shaped button had a long post on the back that was pushed through a hole and then a washer was pushed on behind the leather and the end of the post was cut just proud of it and peened over.
I'm sure the type I describe goes back much farther, but my area of research in original military equipage only goes back that far due to a lack of any good examples I've had access too. I've seen them with ball ends, flattened ends, and more pointed ends and made from brass, copper, iron and lead/pewter, with brass being the most common I've encountered (pre 20th Century).
