You may actually split a 4 conductor humbucker - but having said that, I'm not sure it would sound "nice" or useable.
I had a pair of DiMarzios (DP196 and 197) in a Melancon which were absolutely useless when split...
But, YMMV, etc...
coil tap: where a SINGLE coil has 3 conductors......at one end of the wrap a wire to be used as ground, then one at some point BEFORE the end of the wrap, then one at the end of the wrap. So you can select 2 different amounts of wrap for 2 different outputs. Say for example, a 5k tap, and a 8k tap. So you have a SC that can be switched from a low vintage output to a very hot one.
Split: a double coil pup that when SPLIT grounds one coil out so you're left with one, giving you a SOMEWHAT SC type sound.
I realize most know this, but i see the phrase "coil tap" used so often to describe splitting i just had to describe the 2.
I've never found a SC sized hummer that sounded good when split. But then i never found one i liked period. But as full sized ones go, as leonc said elsewhere, the andersons split pretty nicly. The H-2 being the one i have. Still not a great SC sound to my ear but better than most. One reason most hummers don't sound totally SC-like when split is because even when you split a humbucker and one coil is electronically no longer in circuit and doesn't affect the tone at all, the polepieces for the non-working coil are still picking up some string vibration because they are attached to the same magnet as the working coil.
there are none in lipstick size.
Humbuck type I can only think of let's see
DiMarzio Fast track style (these are blades I think they can be split)
Seymour Lil '59 (although someone said these aren't very good)
maybe a screaming deamon?
This is my preference also.
I try to utilize the different sonic quality and emphasis it by picking dynamics.
In most live situations, that is sufficient for my requirements. And a big AND, the pup remains hum bucking!
With a humbucking pickup you can have it wired in series or parallel.
Tapping a pickup is the term where a single coil has wraps and a lead partially through the entire wound pickup, and the lead at the end of the wrap for the full single coil sound.
If you have a stacked single coil pickup, where two separate coils are involved, you can split that to single coil, if you have the 4-conducter leads coming from it.
As mentioned, the Seymour Duncan site has many wiring diagrams on how to wire up different sounds from their pickups.
On the single coil-sized humbuckers, I agree that parallel sounds better to me than split, plus, it stays hum-cancelling. Any 4 conductor pickup can be split, though. Tapping is something else entirely, as was stated. Many people confuse those or use them interchangeably, but electronically they are very different.