At this point in the search I think the true author of "Gideon's Band" is probably unknown.
Gus Meade, in his Country Music Sources, lists only the attribution to the arranger, Charles R. Dodsworth, 1861. That's the first occurrence of the song listed.
It seems to have come out of the minstrel shows of the mid-19th century, and I seem to recall hearing it has had a long and illustrious, if somewhat obscure, career sung by men's clubs, fraternal organizations, etc.
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sj