I feel like this may be one of those questions that's either very thought evoking, or really stupid. But: should we expect a difference? Does "humbucking" in and of itself change the tone of a pickup?
When comparing a typical single coil to a typical humbucker (say, a tele pickup to a PAF style humbucker, or a Jazz bass pickup to a typical two-coil soapbar humbucker), my impression was that the difference in tone was more from the difference in sensing width along the string and coil shape, rather than just the fact that it's a humbucker. With that in mind, my thought for this electromagnet pickup was a typical two coil side by side arrangement where each coil senses the whole string and you could turn off one coil completely (the coil and the magnet).
I have made lots of plain old single coil Jazz pickups, and several split coil pickups that are essentially the exact same construction, just with the flatwork cut in half so you can wind two coils instead of one. This strikes me as more or less equivalent to your idea. I've never directly A/B'd them but I guess my question is, SHOULD there be a difference?
But I'm also starting to wonder if this would all be worthwhile at all or if there are better ways to get there. Besides the sensing width in terms of the magnet, I'm really starting to become more of a firm believer that the size and shape of the coil is important. I've recently built a new ukulele pickup that's a straightforward two-coil blade humbucker. I've made other uke humbuckes, typically as miniature versions of a guitar PAF humbucker, and they sound like you'd expect them to - like a Les Paul or other Gibson. Meanwhile, this new pickup is pretty different. The two coils are very thin (wrapped on 1/16" steel blades) and very tall (a hair more than 5/8") as compared to a PAF. The pickup sounds totally different, despite having the same magnet and the same number of turns as the PAF style pickups. If you close your eyes, you'd swear it was a twangy single coil telecaster pickup. It just sounds like a narrow single coil pickup despite being a humbucker. I've also recently built a Jazz pickup that's as short and fat as I could fit in the shell. Same number of turns and same magnets as other J's I've built, but it has a pretty different tone. Next up I'm going to try the opposite on a P pickup - make a skinny tall coil, and see if I can get something different than the typical P - my goal is to imitate the brighter, more balanced tone of an underwound P, but without the potential loss of output level. If that works (and I'm confident it will), I want to put two skinny tall coils in each P shell, and then set them up so it can be "coil tapped" by turning two of the four off. I figure that'll give the most versatility possible in a P format.
Yeah, I completely agree. When most folks compare Single Coil and Humbucker pickup sounds, they really mean Fender Jazz vs Fender P-Bass. But the Fender Jazz and Fender P-Bass pickups are very different in their internal geometry, in ways that significantly change their sound. They are two different pickups, regardless of whether they are single coil or humbucker.
You can build a split-coil humbucking pickup with Jazz coil geometry, and it won't sound that much different from a single-coil Jazz. Likewise, a single-coil with a short wide P-Bass style bobbin will sound more like a P-Bass than a Jazz.
The geometry of the coil, and how it fits within the magnetic field, is more important to the overall sound of the pickup than is the choice of single coil vs split humbucker.