On the authority of A World Reknown Folklorist, the song in question is Pliney Jane. Until I met Grandpa a few years ago, I had always considered him mostly a comedian. After listening to him live, I started listening to records and gained a much greater respect for his music. He was a world class comedian, but no slouch in the singing and picking department either. His son is the better banjo player though.
The Tribute which Dale mentioned is at the Ozark Folk Center in Mountain View, Arkansas on Labor Day weekend. David Holt has been boning up on Grandpa's songs and who knows, maybe Pliney Jane is now in his repertoire.