Interesting find. I keep coming back to it. This isn't much help, but some observations in case it helps somebody:
1. From the engraving/stamping on the back, it would appear to be not mounted on something (maybe a badge, necklace, or some other unmounted item).
2. If it's a handshake in the image, the left "person" is using a two handed shake. That said, they have an odd hand in that it looks like their right hand has more than four fingers. The left hand (of the left hands) is for sure a hand.
3. There's an NC or NG on a ribbon above the hands.
4. From the kerning (spacing between letters/numbers), I would have thought we could see part of the 8 if it was 1856. There's a little circle (almost degree mark) high left of the #5, but that's not part of a number 8 (could be part of the image above it). It's not super rare to separate numbers (like 18 56), but not really common either.
5. 1856 was an election year so it could be an election related item.