I still don't get the whole sounds like the wood it's made of description of woody.
In a word Synergy !
On some occassions ( not all that common ) a pick up when mated to a guitar picks up the resonance , color, flavor and sound of the wood.
There's no guarantee that if you swap out a pickup of one guitar (that together produce a woody sound) and put it in another guitar that you'll get a woody sound.
It's a not too common mating or combination of pup and guitar.
Doesn't that mean transparent?
No.
Transparency is a quality of a pup to capture faithfully the sound of the strings with great clarity, detail and definition.
A friends Epi Riviera equipped with minihumbuckers (very transparent pups)
doesn't produce a woody tone.
So if you had a lucite guitar with a really woody pickup, it would sound like lucite?
Chances are not.
Once again it's a synergy or mating or interaction between a pup and the guitar it's placed in . There's no guarnatee that a pickup that sounds woody in one guitar will sound woody in another.
I love this debate, because the term is all over boards like this, and there seems to be two camps. One with a specific sound in mind, and the other with the transparency slant. If we get this, it's on to world hunger!