One pickup, two very different sounds
Basically, any pickup that has 4-conductor wiring can be split. What this means is if you are holding the pickup and the wire that comes out if it has four smaller wires coming out of it, then it has 4-conductor wiring and can be split. If the pickup has only two wires, or the standard braided wire with one smaller wire coming out, it cannot be split. That was a very layman’s explanation, but I’m trying to keep this all helpful and not get too nerdy.
Some have asked me to recommend a specific pickup for splitting. Instead of recommending a specific pickup, and there are many many many (many) aftermarket humbuckers out there, better to understand this: If you would like to possibly purchase a humbucker, you should have no trouble finding out from the company’s website or the package of the pickup if it has a 2-wire lead or a 4-wire lead.
The simplest way to think of it is that a 2-wire lead means a pickup has only one possible sound. A pickup with a 4-wire lead has TWICE the wires, so, twice the potential sounds (a bit silly of a way to look at it, and actually you could have up to three sounds, but hopefully that is an approach that makes it simple to digest)
Most (not all, but most) Seymour Duncan and Dimarzio pickups have 4-wire leads. Most traditional Gibsons have two, and most traditional Fenders have two.
Also, keep in mind that when you want to split a pickup, you need to add a switch to the guitar so that you can switch between the two different sounds. Usually, a mini-toggle switch is installed. Some have asked about doing so with a Les Paul. Most folks (including me) would not want to drill any holes into a Les Paul. So, you could also have a push-pull pot installed in the place of one of your tone pots. That way your tone control becomes a pickup splitting switch (i.e. pull for humbucking, push in for paralell wiring), with not cutting into the guitar.
What the two sounds are like:
As far as the sound. It’s pretty simple. One sound is always “Series” or Full Humbucking mode. That is the pickup in full output mode. The other, and most common option, is “Parallel” wiring, and that will decrease the output of the pickups noticeably, and the pickup will have a softer, more single coil sound. It won’t sound exactly like a strat or anything, but the sound is more bell like, and more open. These two sounds are quite different when you hear them.

