And, here's how you connect the inside coils in series:
Again, you could leave the Red wire of the Neck pickup connected to the output. Sometimes you can't switch every wire you want in a given switching setup & have to leave some things connected. It's not best practice to leave one end of a pickup connected to the output, but it is done when you can't get around it.
You'll notice that we have the same issue regarding magnetic polarities with the series connections. They are in phase electrically, but they will not be hum cancelling.
So, if you decide to flip the magnet on the Neck pickup (for example) to rectify that, then the pickup leads flip electrical phase.
You will end up with something like this:
Then, all of the above drawings have to be modified to reflect that change of electrical phase or all of the connections between pickups will be out of phase.