This is an amusing song, with mostly auto-rhymes, words repeated for easy perfect rhyming as in the opening verse’s terminal “line”/”line”/”line”:

Well, I’m walkin’ down the line
I’m walkin’ down the line
An’ I’m walkin’ down the line
My feet’ll be a-flyin’
To tell about my troubled mind

But the repetition in each verse of three in a row terminal exact ending words seems to prepare the reader for the last two lines with terminal rhymes matching the repeated words, in this case, “flyin'” and “mind,” an interesting rhyme because -ind of “mind” looks like it would rhyme with the -in” in mind, but it does not; the rhyme is with the -mi in “mind.”

This pattern continues, but for one exception in verse 6 where “because” has no rhyming partner:

I see the morning light
I see the morning light
Well, it’s not because
I’m an early riser
I didn’t go to sleep last night

It stands out in this way, and for me, it stands out as the most entertaining of all the verses.

Not to be lost in all the “walkin’ down the line” that appears in the song is the walking down each line that the poet is doing to get to a line that breaks the repetition, as if he’s waiting for someone to give him that one original thought that he craves in “Brownsville Girl”:

Now I’ve always been the kind of person that doesn’t like to trespass
but sometimes you just find yourself over the line
Oh if there’s an original thought out there, I could use it right now

Over the line, (get over the line already!) over that “Walkin’ down the line” line is a rhyme that awaits that won’t merely repeat.  The pattern works–it’s bluesy humorous.

And the humor is worth reveling in as well as how simple it is, as Arlo Guthrie and Pete Seeger get across in this live 1975 recording of it:

And here’s Arlo singing the “Bobby Dylan tune” at Woodstock: