From the clothing I'd say 1910, give or take 20 years. I assume it is a political button (governor, president?). If he had a center part and a greyer walrus moustache, I would guess William Taft. Does anyone recognize him.
I don't know why I bought it other than I thought it looked cool. The button is 1 5/8" celluloid over paper by Whitehead & Hoag, the same company that made the inlay in the jockey chip.