Performing on Oscar Brand's "FOLK SONG FESTIVAL," WNYC, Oct 29, 1961, Bob Dylan introduced "The Girl I Left Behind" as follows:
"...this here song's a good example. I learned it from a farmer in South Dakota, and he played the autoharp. His name is Wilbur. Met him outside of Sioux Falls when I was there visiting... people an' him... and heard him do it... I was looking through a book one time, I saw the same song and I remembered the way he did it. So this is the song."
The book Dylan was "looking through" was most likely Alan Lomax' The Folk Songs of North America, Garden City, 1960. His version is very close to that published as No. 165 on pp. 318-320.
The song itself goes back to the British Isles. An Irish version, collected from G. B. Newe in 1927 can be found in Digital Tradition (filename GIRLLFT6).
From Alan Lomax' notes (p. 307):
The narrator leaves Ireland for Scotland, or sails from England bound for Amerikay, sets off on horseback from Virginia to Tennessee, turns west from Tennessee to Texas or old Missouri, or starts across the plains from Texas to Salt Lake City or California. In British versions he often finds a new sweetheart whose gold destroys his love for the girl he left behind. News then comes that his parents and his old sweetheart have died of broken heart. In all American versions, however, the man is betrayed by the fickle girl he has left behind...The song is also known as "Peggy Walker" (collected in Missouri) and has been recorded by old-time musician Buell Kazee as "The Roving Cowboy" on Brunswick 156-A.
One further variant, recorded as "Maggie Walker Blues" by Clint Howard (vocal and guitar), Fred Price (fiddle), and Doc Watson (guitar) on "Old-Time Music at Clarence Ashley's" (Folkways FA 2355, 1961) and credited to T. C. Ashley (Clarence Ashley) is sung to a tune that is basically that also used by Kelly Harrell for "My Name Is John Johannah" and by Dylan for his "Long Time Gone" (copyrighted on Apr 11, 1963 -- Clinton Heylin, Stolen Moments, London, 1988, p. 322).
Furthermore, parts of the lyrics are rather close to those of "Maggie Walker Blues," as the following example should amply illustrate:
LONG TIME GONE
My parents raised me tenderly,
I was their only son.
My mind got mixed with ramblin'...
MAGGIE WALKER BLUES
My parents raised me tenderly,
They had no child but me.
My mind being placed on rambling...
Obviously, the "My parents raised me tenderly..." lines seem to be commonplace "floating" lines which can be found in several folksongs ("The Bold Deserter" being one further example):
My parents reared me tenderly,
I being their only son,
But little did they ever think
Tthat I should follow the drum...(Digital Tradition filename BOLDDSRT)
The similarity of the tune, however, and the "fickle girl" image also found in "Long Time Gone" make the Clint Howard version a rather likely folksong source for Dylan's "original."