In 1962, Origin Jazz Library released the album Henry Thomas Sings the Texas Blues.
It included his "Honey, Won't You Allow Me One More Chance", which was presumably the source of Dylan's version.
[1]: 43 Todd Harvey, in his book The Formative Dylan: Transmission and Stylistic Influences, 1961–1963, analyzes how Dylan dropped Thomas's verses, and adapted his choruses, utilizing Thomas's AAAC rhyming structure and four 4-bar phrases in 2/4 time.
Harvey writes: "The text of Thomas's chorus remained constant throughout the song.
He increased Thomas's tempo and added his own guitar accompaniment, placing harmonica solos between verses.