Both songs are put together from "Brother Eben's Got a Coon," and verses borrowed of parodied from a number of other songs. A Negro folk song version was collected in 1909 by Perrow. The Traditional ballad Index refers to a song from 1878 by Bob Allen, "Old Uncle Eph."

Uncle Eph'm got de coon and gone on, gone on, gone on,
Uncle Eph'm got the coon and gone on,
And left me wathing up de tree.

Newman I White, in American Negro Folk-Songs, 1928 (1965 reprint) says Perrow has this refrain after a stanza that has antecedents in old minstrel books, so the blackface minstrels may have been the source of the song. (White, # 37, p. 223)
Scarborough, 1925, found the same refrain, also in combination with old minstrel songs from the 1840s-1850s:

Brother Eben's got a coon,
And gone on, gone on,
Brother Eban's got a coon,
And gone on, gone on.

OLd Dan Tucker, Possum Up a Gum Stump, Liza Jane. Shake dem 'Simmons and a parody of Golden Slippers also have contributed.

The Traditional Ballad Index, cufresno, lists some recordings.