I think it was Mance Lipscombe who used to do a version of this tune. The verse I remember went…

Which a way, do Red River run?
Which a way, do Red River run?
Run out my back door and gone.

I've never learned any more of it but used to use it to give beginning students a simple exercise to show how finger picking works. Lipscombe played the whole thing out of an E chord. There was an ocatve bass and a sparse melody that could be done on the beat using a pinch or played off the beat.

I haven't heard the Lipscombe track for a large bunch of years so I may just misremember how it went.

      - Mark