I sent a message to Ibanez customer support, but I'm not expecting an answer from them.
I found a schematic for the older 90's ATK's, and one of the newer ATK100, but can't find one for the 3EX1 like I have. Also, on the one for the older ATK's, the switching pcb isn't mapped out so I can't tell what wires are what from the pickup.
I know the "triple coil" pickup is actually a humbucker with a dummy coil, but what wires do what?
I also found this:
I understand black is a ground, because there's a shield wire as well. I'm guessing red is the hot output from the northmost coil, because it's wired to the switch and then that goes out to the preamp, and according to that diagram of the switch, the neck coil is always on regardless of position.
Other than that, I can't tell too much what wire is what.