Re: Pickup choice for coil tap
So the characteristics of the humbucker un-split stay pretty much like they are but just get thinned out?
A normal installation of this type would have the humbucker as its normal self as the default.
You would flip a switch or pull/push a pot to split it so only one coil is operational (your choice as to which one). This would be literally half the pickup, so, yes, the sound will be thinner. Sometimes that thin sound is very usable or even desirable. I have never split a JB, for example, but by many accounts it is a fine-sounding single coil in split mode. I've never played a Stag Mag, but it's designed to sound like a Strat pickup when split.
Some pickups have mismatched coils where one coil is hotter than another. So splitting to the hotter coil will yield more beef/less of a volume drop in split mode. To my knowledge, Seymour Duncan only has two pickups with this construction, the Custom/59 Hybrid (splitting to the Custom yields a somewhat Tele tone, to my ears), and the P-Rails (which usually gets split to its P90 half).
Generally, the hotter the pickup, the more usable the split sound is b/c it's half of something big, not half of something small. That said, there are some hot pickups that don't split well, and there are some low power winds that split well (Pearly Gates comes to mind). Because split is not the primary application of 99.9% of humbuckers, you may have to experiment a little (or Google a lot, heh) to find humbuckers that perform well in secondary applications.