But, yes, there existed tokens of the type you show. For the history of the campaign, see:

https://en.wikipedia.org/wiki/Grover_Cleveland_1888_presidential_campaign

Your token, if it were complete, would have a brass eagle with safety-pin on top so it could be clipped to, say, a jacket, and the medallion would dangle.

https://usamericana.com/products/cleveland-thurman-democratic-candidates-white-house-1888?variant=32356546478162

But take heart: Grover got his revenge and returned to The White House in the 1892 elections. Rrrrrrooaarrrrr!