The second coil of wire can't do anything but be a parallel coil that's stacked. A phantom coil requires that no magnet be inside the coil, otherwise it'll generate signal. It cannot be a humbucker because, being on the same magnet, the magnet poles can't be reversed inside the second coil.
So it's a stacked parallel pickup.
Change my mind.
That's not really true. The stacked coil design is definitely 100% a true humbucker.
When you're talking about humbucking, you can literally ignore the magnet. Forget it exists. It does not matter in terms of how the coils pick up noise, and humbucking is all about taking advantage of the noise signal produced by two separate coils. To humbuck, all you need to do is have the two coils pick up noise that's out of phase. When you have two coils that are physically oriented the same, to make them humbucking you reverse the wind direction, (or reverse the leads) such that current flows in the opposite direction. Reversing the leads effectively reverses the wind direction, so either way you end up with two coils that are effectively reverse wound. Noise will generate a signal (current) in both. In one of them, it goes "left to right" and in the other it goes "right to left" and as such the two currents cancel each other out and the net current (outside the pickup, to your controls) is zero. (it's an AC current of course, so it's really phase and not direction, but you get the point).
That's how all humbuckers work, magnetic field or not. You can take the magnet out of a pickup, or put in two magnets, or put the magnet in sideways, or whatever you want, and the pickup will still buck hum.
The magnet is only important in terms of the coils picking up the signal from the string. Noise creates a signal in wire whether there's a magnetic field or not. Strings can only create a signal if there's a magnetic field, and both the string and the coil are in the same magnetic field. The phase (direction) of the current is determined both by the direction of the coil wind, AND the relationship between the string and the magnetic field AND the coil and the magnetic field. Does anyone remember the "right hand rule" from high school physics? It helps you remember the direction the current will flow when a conductor is moving in a magnetic field. If you want both coils to contribute to the signal, and you want the contributions to not cancel each other out, and the coils are reverse wound, you need them to be in opposite polarity magnetic fields. Magnets have a north and south end, and every magnetic field has regions oriented towards both, so even with a single magnet you can still have humbucking coils. In a stacked coil humbucker like the EMGs, the two coils are essentially sitting on either end of the magnet - one is wrapped around the north pole and one around the south pole (pickup magnets are magnetized "sideways" compared to most typical general-use magnets). So they're not in equivalent positions magnetically even though they're on the same magnet.
At any rate, in a stacked coil pickup, the bottom coil is so far away from the strings that it typically barely contributes to the signal anyways, and generally has a bigger contribution just by loading down the top coil (because of the resistance in the coil) rather than actually adding signal. So ultimately it doesn't matter if it's magnetically in the right phase or not, since it basically only exists to create an out of polarity noise signal and also color the tone a little by loading down the top coil. This is why a stacked coil design often sounds weaker and middier than a side-by-side humbucker, you're really only getting one coil's worth of signal plus a little frosting on top. But considering EMG's design with the built in preamps, they're able to compensate for that and still get the tone they want, compared to some other stacked coil designs which have generally been much less popular (usually because they sound a little weak). Lots of brands have tried to make stacked coil pickups (especially for the strat/tele market) and they have generally not caught on very well.
EMG on the other hand have done a really good job of making a comprehensive design where every choice was made with the whole design in mind, rather than just slapping a preamp on an existing pickup design. They basically wrote the book on how to make a good sounding stacked coil pickup. One of the Turners (I forget which one) worked at Fender prior to EMG and had worked on the (stacked coil!) Fender noiseless pickup designs. It's pretty easy to see their current stacked coil designs as the evolved version of the Fender pickups.
