Parallel Anthology Track 63
Track 63: Bascom Lamar Lunsford - I Wish I was a Mole in the Ground Brunswick 219-B; Recorded in Ashland, Kentucky, April 1928
Record label does not assign authorship, nor do the notes in either Anthology booklet or www.78discography.com.
Lunsford said of this song, "I've known it since 1901 when I heard Fred Moody, then a high school boy, sing it down in Burke County." , calling it "a fine type of indigenous American banjo song extant in the Great Smoky and Blue Ridge mountain region of the south, and has numerous unrelated stanzas born out of the hilarity of mountain banjo 'picking." 
These are good grounds for treating this composition as public domain.
Mole in the Ground by Logan English album released in 1962 (according to folkways.si.edu): Spotify According to this album's liner notes, credit for this version is assigned to Bascom Lamar Lunsford, with the exception to the lyrics of the last verse.
Mole in the Ground by Basom Lamar Lunsford album released in 1953 (according to folkways.si.edu): Spotify Lunsford never claimed credit for writing or arranging this song (see above)