I found a button sort of thing that I first thought was a button from a old pair of bibs.
Upon further inspection it is not what I thought.
The front of the button like thing says GUT HEIL. Under that is the image of a handshake and under that the letters E. T. V.
The back of the button thing looks like the head of a thumb tack and it screws off.
Now you have 2 pieces.
The back of the front piece has a symbol that looks like 2 acorns joined at the top of the cap.
Inside the nut part of the symbol are the letters I on one nut and U on the other.
The back also has a screw with a pointy spike like thing. I assume the spike is to prevent the button from turning.
The back has no distinguishing marks and is just the female threads.
From what a short search of the German-language Web shows, “Gut Heil” seems to have been a slogan/greeting of the 19th century German Turner movement founded by Jahn. A number of sports clubs still have this slogan as part of their name. The slogan seems to have been coined early enough to also have been used by German-American sports clubs. The handshake symbol was a frequent symbol of associations, often but not exclusively used by socialist associations/clubs (pre-1933 German sports clubs were often explicitly or implicitly affiliated with the socialist or nationalist-conservative camp).
Of the “E.T.V.” the “T” probably is an abbreviation of “Turn-” or “Turner-” (i.e.: gymnastics-/gymnasts-), and the “V” probably abbreviates “Verein” (club) or “Verband” (association)
So this may have been some kind of membership badge or button of a German-American or German/Swiss/Austrian sports club.
I googled gut heil and even found E.T.V. but I don’t speak german so I don’t know who is being wished good luck.
I had thought of a tie tac but the fact that the thing screws on and the screw is about 1/8 inch makes me think it isn’t a tie tack.
Maybe a lapel pin?
The front of the button is 11/16. The back is 9/16.
The front of the button appears to be a yellowed B&W picture covered with a clear plastic.