So, coil 'B' has been shunted and Coil A is the active coil. If we wanted Coil 'B' to be the active pickup, is there a way to do this? Sure.
The previous diagram had a conventional wiring - red to 'plus', black to 'minus' and the two
'middle' wires (black and white) connected to each other. The graphic on the right shows an
alternate wiring. Speaking informally, you could say the red and the green wires are now
the 'middle wires' and what were the two 'middle wires' are now on the 'outside'. (I refer to this as
'inside out' wiring.) There is nothing wrong with this, it sounds exactly as it did before
and it is in phase with itself just as if it were wired conventionally. The difference is that
with the coil cut switch 'on', the red wire
is being led to ground, Coil A has been shunted and
Coil B is the active coil.
When the coil cut switch is 'on', a conventionally wired humbucker 'grounds out' the middle wires and Coil A is the active coil. If the humbucker has an alternate (or 'inside-out') wiring, Coil B is then the active coil during coil cut.
The diagram on the right offers an interesting, relatively easy-to-wire circuit that gives you three tone choices with just one switch. Remember to use a single pole double throw center OFF switch. (This switch isn't particularly difficult to find but make sure you use this exact type of switch).
In the center position, the switch isn't connecting anything and so this produces the series wired humbucker tone.
When switched in one direction, the switch connects the red and black wires, which shunts Coil A and leaves Coil B active.
When switched in the other direction, the switch connects the white and green wires, which shunts Coil B and leaves Coil A active.
Looking very carefully at the graphic, there is a dashed blue line in the lower left and upper right part of the switch. These are the terminals that are connected when the switch is in the middle ('coil cut') position. Notice that in this case, the switch does not shunt the inactive coil but in fact shuts it off. (Coil B's white wire has no connection to the output). Following the current flow, we see that Coil A is the active coil.
Now, if we want Coil B to be active, we'll have to give the humbucker an 'inside-out' wiring.
Compared to the last diagram, it's as though the green and red wires have been shifted 'up'
one terminal and the black and white have been shifted 'down'. Parallel and series settings
will sound exactly the same as the previous wiring. The
only difference is when the switch is set to the middle 'coil cut' position Coil B is the active coil.
And you know the way to 'choose' which coil stays active, right?
Conventional wiring - Coil A is active with coil cut switch 'on'.
Alternate wiring- Coil B is active during coil cut.
2) The second reason for selecting a particular coil (actually set of coils) is that if it is done in the proper
way, the result is yet another humbucking pickup. (And you thought your guitar only had two humbucking pickups huh?)
However, there is a way to choose an active coil by switching. Looking at the diagram, if you wire a phase switch along with a coil cut circuit, you will be able to choose the active coil without rewiring anything. When the upper terminals of the phase switch are conducting, Coil A is the active coil. When the bottom phase switch terminals are conducting, the red wire is connecting to ground and the green wire is going to the '+' connection. Because of this, the coil switch now grounds out the red wire and so Coil B becomes the active coil.
Another way to choose active coils by switching is using 2 SPDT switches. To see diagrams for this, please go to page 5 and scroll down ⅔ of the page and read the 'How It Works' section.
Yet another way to choose active coils by switching is wiring a double humbucker guitar for Super Seven Switching. Of course this is very involved and not something you'd want to do if you just want a coil cut switch and nothing else.
Good luck with the guitar rewiring.