Found in gaylord mi on a very old dentist property I've been told the dentist use to service the army soldiers on their way to the Mackinaw fort that closed in 1895 That was part of the 1812 war but gaylord was a old logging town also. I bin to the historical society and they are very interested in they believe it to be very old And the back screws on
Maybe it is for the Railroad Telegraphers Union. I found this ad from the 1907 "The Railroad Telegrapher" - a sounder is a telegraph machine and when I looked at photos of some they did resemble the object on your piece.
The closest I could find for a pic of the what might be on the button - so far - is this medallion.
8. LIRR Union pins. Order of Railroad Telegraphers is in the center of the display (the sounder within the wreath) (J. Skinner and G. G. Ayling collections)