In 1792, the dramatist and song-writer Charles Dibdin wrote a play called The Quizzes, which included this song. A later compendium of his songs gives it the title "Etymology of Quiz", but it isn't really about the etymology at all. However, it is very similar to another song written a couple of years previously.
The Professional Life of Mr. Dibdin, Volume 3—Charles Dibdin (1803)The Quiz
The word Quiz is a kind of a sort of a word
That often applies to some being absurd;
One who seems as 'twere oddly, your fancy to strike,
In a sort of fashion you somehow don't like:
A mixture of odd, and of queer, and all that
Which one hates just, you know, as some folks hate a cat:
A comical, whimsical, strange, droll, that is
You know what I mean; 'tis—in short 'tis a quiz.
It matters but little, by what I can hear,
What a Quiz's endowment are, for he's but queer:
As order from chaos, they tell us began.
So a very queer quiz may be yet a good man:
A parson, for instance, though pure, word and thought,
Mild as mercy, and good as the truth he has taught;
Should he wear a strange wig, or possess an odd phiz,
He'll be scouted at once for a monstrous quiz.
At this same play of quiz each loses and wins.
Ins are quizzes to outs, and outs quizzes to ins:
Honest men are all quizzes to rogues;—then again,
All rogues appear quizzes to all honest men.
Beaux are quizzes to slovens, and slovens to beaux.
Rich to poor, poor to rich, and 'tis thus the world goes;
In short, every creature to some other is—
The present company excepted—a monstrous quiz.
But lest having chaunted of quizzes too long,
You begin to think this but a quiz of a song;
While your suffrage to night I most humbly implore,
I conclude, with your leave, pointing out one quiz more.
About two hours hence—if in any one here
Strong symptoms of yawning begin to appear,
The natural conclusion in such a case, is
That he—oh, no—I—must be set down a quiz