I’ve seen buttons with figures riding on a goose or swan, but usually they’re cherubs or occasionally Aphrodite. That appears to be neither of those and does indeed look like a clown-type figure on a goose rather than a swan. If you zoom in, the mouth looks like he’s laughing out loud. Perhaps related to this (from the Wiki entry on “Circus Clown” ?
“The slapstick form known as pantomime had been a Broadway staple since before the Civil War, but it reached a peak of popularity during the 1860s and 70's. These shows placed figures from Mother Goose stories in wildly varied settings, always finding an excuse to transform them into the clown characters of traditional commedia dell'arte (Harlequin, Columbina, etc.). Popular songs were loosely inserted whenever the audience needed a breather. Lavish sets and athletic clowning were expected, along with elaborate ballets.”