The Red Clay Ramblers rendition sounds just like the one sung by Fred Price, Clint Howard and Doc Watson, which can be found on the Smithsonian Folkways collection Classic Mountain Songs The liner notes say it was a spiritual learned in childhood, and was composed by G.T. "Dad" Speer, leader of The Speer Family gospel group (no date given.)

You can find a set of lyrics on the liner notes to the New World collection Hills and Home: Thirty Years of Bluegrass (PDF), where it is performed by the Stanley Brothers and the Clinch Mountain Boys (from a 1959 recording). The copyright notice reads:
(c) Copyright A 312668 La-Car Publishing Company
I suspect that the vocal arrangement used by all three of these groups originated with the Speer Family.

A solo rendition can be found online at the John Quincy Wolf Folklore Collection of Ozark Folksongs (click), including an MP3. It's rather abridged in comparison.