From your pic, the red and blue wires twisted together are the end of the first coil and the start of the other coil, leaving white for hot and black and the bare wires for ground. This would be for typical series humbucking mode.
If you want to do a series/parallel or coil tap, then you'll need to disconnect the red and blue wires and wire them to a switch/pot. From what I'm seeing in the pic: white=hot and red would be the end of that coil/ground and the next coil would be blue=hot to black for the end of that coil/ground.
What I would suggest is wiring the pickup to a 4-way selector switch to 1 volume and 1 tone w/cap, then to the jack. Wiring the HB to that switch as 2 singles would be easy and allow you to play either coil separate, both coils together in parallel or both together in series.
I think I bought the same part, one pre-wired and one just the pickup. Here is the wiring diagram, hopefully without errors. I was wanting to split the coils of an old Epiphone humbucker and use this wiring.