This word for a pun, a hoaxing question or a conundrum pops up first in Ben Jonson’s play Bartholomew Fayre of 1614 and appears a few times afterwards, but is effectively extinct by the middle of the nineteenth century.
Notwithstanding the advantage which this age claims over the last we find Mr. Dryden himself, as well as Mr. Jonson, not only given to Clinches, but sometimes a Carwichet, a Quarter-quibble, or a bare Pun.
London Magazine, August 1824. The writer is paraphrasing a line in John Dryden’s comedy The Wild Gallant of 1662 in which these forms are given as examples of dubious wit. A clinch was a type of sharp repartee or word-play; a quarter-quibble was a poor or weak quibble, a quibble at the time being a pun or a play on words. Dryden’s use of pun was among the earliest in the language.
The origin of carwichet is obscure, though it has been suggested that it comes from colifichet, a French word of the time for a fantastic small object of no great value, but which now means any knick-knack or trinket (it’s said to be from the older French word coeffichier, an ornament that was fixed to one’s hat).