There's a ton of stuff here on this subject. The Advanced Search feature can supply you with plenty of reading.

You want 4-wire pickups for advanced switching designs.

Humbucking pickups built for coil-tap simply provide a wire from the connection between the two coils, allowing you to short out one of them. This leaves you with a single coil. And noise problems.

A 4-wire pickup allows you access to both ends of both coils, for connection any way you want. You can still coil-tap, plus you can coil-split (which means using one coil from one pickup with one coil from another pickup), or connect the coils in series or parallel.

You can see schematics of all this and more by going to the >DiMarizio< website and navigating to the wiring diagrams in the humbucker descriptions.