Go limber, Jim: you can't go.
Go weave and spin, you can't go, Buckeye Jim.

This chorus is what ties together "Limber Jim" and "Buckeye Jim". It doesn't actually call him "Limber Jim", but says "go limber, Jim". But we do know that there was the earlier "Limber Jim" song from Ohio.

In another thread back in February called "Buckeye Jim: Oddest Lullaby I've heard" (I won't try to blue click it since I can't seem to make that work), someone suggested that maybe Buckyed Jim was from Ohio, since Ohio is the "Buckeye State". I wonder when Ohio came to be known as the Buckeye State. We do know that "Limber Jim" hung out in Cincinnati, according to Lafcadio Hearn. Perhaps he did pick up an additional nickname.

I've only found two other references to "buckeye" or "buck-eyed". One is the song "Big Eye Rabbit". A version from Alabama goes as follows:

I wanted sugah very much,
I went to Sugah Town
I climbed up in that sugah tree.
An' I shook that sugah down.

CHORUS:
Buck-eye rabbit, Shoo! Shoo!
Buck-eye rabbit, Shoo-dah!
Buck-eye rabbit, Shoo! Shoo! Shoo!
Buck-eye rabbit, Shoo-dah!

I went down to my sweetheart's house,
I ain't been dah befo'
She fed me out of an old hog trough,
And I don't go dah no mo'!

Way down yonder on Cedar Creek,
Where all them gals grow 'bout 'leven feet,
Jump in the bed but it ain't no use,
Feets stick out like a chicken roost.

[From: p. 120 of FOLK SONGS OF ALABAMA, Byron Arnold (University of Alabama Press, 1950). Reprinted in Alan Lomax's THE FOLK SONGS OF NORTH AMERICA, #266, p. 504]

Note the "trough" and the "way down yonder".

Thomas Talley also has a version called "Buck-Eyed Rabbit! Whoopee!" (#269, p.149, THOMAS W. TALLEY'S NEGRO FOLK RHYMES): last verse only

Buckeyed Rabbit! Whoopee!
Buckeyed Rabbit! Ho!
Buckeyed Rabbit! Whoopee!
Squir'l's got a long way to go.

It is not clear which came first, "buckeyed" or "big-eyed". Mellinger Henry has a different variation of "Big-Eye Rabbit" (#173 FOLK-SONGS FROM THE SOUTHERN HIGHLANDS, 1938), obtained from Mr. C.L. Franklin, of Crossnore, Avery County, North Carolina, "who learned it when a child from his father, William Franklin." Henry does not give a date.

Big eyed rabbit behind the pine;
Big eyed rabbit, you are mine.
Rabbit skipped; rabbit hopped;
Rabbit ate my turnip top.
I cocked my gun; the hammer flew;
I tore that rabbit square in two.

My only other reference is to a "buck-eyed Whippoorwill" in a song in Talley's book (#79,pp.51-52) called "Sheep Shell Corn": (first verse only)

Oh: De Ram blow de ho'n an' de sheep shell co'n;
An' he sen' it to de mill by de buck-eyed Whippoorwill.
Ole Joe's dead an' gone but his Hant blows de ho'n;
An' his hound howls still from de top o' dat hill.

So, who knows the orign of "buckeye". It could refer literally to a deer's eye, or to a horse chestnut, or to Ohio, or be a form of "big-eyed", or simply brown-eyed, or it might have a racial overtone, like "Cotton-eyed Joe". There is a "Buckeyed Jim" version in the DT. I am curious as to the sources for both of the versions in the DT. Does anyone know where they came from?