He stood on his head till his waistcoat turned red

Fit the Seventh
THE BANKER’S FATE

489 · · They sought it with thimbles, they sought it with care;
490 · · · · They pursued it with forks and hope;
491 · · They threatened its life with a railway-share;
492 · · · · They charmed it with smiles and soap.

493 · · And the Banker, inspired with a courage so new
494 · · · · It was matter for general remark,
495 · · Rushed madly ahead and was lost to their view
496 · · · · In his zeal to discover the Snark

497 · · But while he was seeking with thimbles and care,
498 · · · · A Bandersnatch swiftly drew nigh
499 · · And grabbed at the Banker, who shrieked in despair,
500 · · · · For he knew it was useless to fly.

501 · · He offered large discount—he offered a cheque
502 · · · · (Drawn “to bearer”) for seven-pounds-ten:
503 · · But the Bandersnatch merely extended its neck
504 · · · · And grabbed at the Banker again.

505 · · Without rest or pause—while those frumious jaws
506 · · · · Went savagely snapping around-
507 · · He skipped and he hopped, and he floundered and flopped,
508 · · · · Till fainting he fell to the ground.

509 · · The Bandersnatch fled as the others appeared
510 · · · · Led on by that fear-stricken yell:
511 · · And the Bellman remarked “It is just as I feared!”
512 · · · · And solemnly tolled on his bell.

513 · · He was black in the face, and they scarcely could trace
514 · · · · The least likeness to what he had been:
515 · · While so great was his fright that his waistcoat turned white -
516 · · · · A wonderful thing to be seen!

Source: The Hunting of the Snark, Lewis Carroll, 1876

In The Natural History of Make-Believe - A Guide to the Principal Works of Britain, Europe, and America (1996), John Goldthwaite wrote (page 158): "I suspect, that the publication of Edward Lear's Nonsense Songs pricked Dodgson's jealousy into play in 1871, the year of Through the Looking-Glass. For the next five years it would provoke him into realizing a book of rhymes bigger, funnier, more nonsensical than anything Lear could dream of making - an epic of nonsense, an Odyssey of nonsense."

Dodgson may have been inspired to take a challenge competitively. I do not think that Dodgson was driven by "jealousy". (I also disagree with another assumption: On page 158, Goldthwaite assumed that C. L. Dodgson casts himself as tragic hero in the role of the Baker, whose "courage is perfect!". Dodgson applied his courage in a much smarter way than the Baker. The dangers of being curageous without caution and without strategy even may have been a topic of The Hunting of the Snark. I think that Dodgson was not so narrow-minded to make himself the hero of his poem. Dodgson was involved in many discussions on contemporary issues.)

I do not believe that Dodgson/Carroll wrote pure nonsense. He could point "to the strong moral purpose of this poem itself, to the arithmetical principles so cautiously inculcated in it, or to its noble teachings in Natural History". He just used different systems of logic. One of them was Lear's nonsense logic: If standing on your head turns your waistcoat red, then fright very well may turn your waistcoat white.

By the way: This possible allusion to Lear's waistcoat nonsense has another advantage: In contrary to me (who easily could add color to Lear's illustration), Lear couldn't use colors when his collection of nonsense went into printing: In Lear's illustration, the waistcoat still was white, not red. However, to Henry Holiday depicting a Banker with a white waistcoat of course was no problem at all.

The Dalenberg Library of Antique Popular Literature (dalenberglibrary.com/blog/2014/4/1/a-sense-for-nonsense-from-edward-lear-to-lewis-carroll-to-dr-seuss#comments-533b6276e4b04f19c3e4ae18, 2014-10-14)
"[...] Lewis Carroll (the pen name of Charles Lutwidge Dodgson, 1832-1898) improved on the nonsense poetry model that Lear established in poems like “The Jumblies.” Carroll’s work incorporates mathematical puzzles, political allegory, and mysterious in-jokes into a more fully realized fantasy landscape. Lewis Carroll’s “portmanteau words” are a lot like some of Lear’s nonsense words (e.g. “runcible spoon”), only with a more complex etymology. [...]"

Lear's Limerick (see speedysnail.com/limericks/metre.html) has an AABBA rhyme scheme:

There was an old man of Port Grigor,
Whose actions were noted for vigour;
He stood on his head
till his waistcoat turned red,
That eclectic old man of Port Grigor.

In "The Bankers Fate", Carroll's rhyme scheme is ABAB ABAB ABAB ABAB AABCCB ABAB AABCCB.
The meter of the last AABCCB verse is six-line anapaestic |··°··°|··°··°|··°··°··°| ··°··°|··°··°|·°··°··°|:

He was black in the face,
and they scarcely could trace
The least likeness to what he had been:
While so great was his fright
that his waistcoat turned white -
A wonderful thing to be seen!

In the lines which I rendered in italics, Carroll uses the "logic" which Lear used in the last lines of his limerick as well.

Wer steht nun wirklich auf dem Kopf - Der Mensch oder die Welt?