Hedy West (and A.L.Lloyd) on her "Old Times and Hard Times" 1965 Topic album have this to say :

"Probably had its origin in a minstrel show song. Many songs traditional in the South were introduced there by travelling "Entertainments", medicine, magic and minstrel shows, which included musicians and singers in their programmes." "I sing here a part of the version of "Brother Ephus" that I learned from Grandma, who sometimes accompanies her singing with banjo, played in a double-thumbing style."

Cheers! R-J