Bruce Marcus, class pedant, here.

Amazingly, the OED has no entry for wythe, except as an obsolete  spelling
for white and with (wythe a brief stopover at withe).

Webster's Third, however, additionally offers wythe as a variant of withe,
a word with several meaning in it's entry; a band consisting of a twig
twisted; a slender flexible branch or twig  used as a band or rope; a
tropical American weedy herb who's stems are used in Jamaica for making
baskets; a boom iron, specifically the boom iron that secures the flying
jib boom; a metal ring or band on a mast or other spar. There are also verb
usage- to withe: to wind or twist like a withe; to bind or fasten with a
withe; to snare deer with a noose of withes.

Only thing is, there ain't a brick or a span of bricks anywhere.

Which, of course, begs the question: Are there other terms of art in the
trades with usage so confined that they do not make it into either of the
two standard reference works of the English language?

I checked about fifteen terms from woodworking and allied trades that
quickly came into my mind as likely candidates. Webster's caught every one
of them, though in one instance, "to stick", which I was checking for two
usage; to pile lumber with sticks between layers; and, to make a molding, I
discovered that Webster's usage for the latter is even more confining than
I have found in common usage. It gives the usage "to stick a molding" as
meaning to produce one by mechanical means in contradistinction to running
one by hand.

Any candidates?

Bruce