The substitution of "Johnson" for "Thompson" was most likely inevitable, for I remember being told that "Johnson" was a broadly used generic name for a fool, sometimes referring to whites but more often to blacks (and thus a racial "code word"), perhaps with origin in minstrel or other early lore.

Just for comparison, a Virginia traditional version from Ben Moomaw, Roanoke, VA, 1954, (from memory):

JOHNSON AND HIS MULE

Johnson had an old grey mule
And he drove him around to the cyart,
He loved the mule and the mule loved him,
With all his mulish heart,

   Lord, that mule did sing-a-me, sing-a-me,
   Quonk! Quonk!
   Hoo-noo-nonna-me, quonk (snort) quonk (snort),
   Curry him down wid a rake.

That old mule chawed with a pair o' hind jaws
On a pair of old dirty socks,
But when he'd chew old Johnson knew
'Twas nothin' but sticks and rocks,

Of all the kickers in the the world
He must have been the best,
He rammed his hind legs down his throat
And he kicked himself to death.