Goal: Invisible mod, using Push/Pull pots, to select between two pickups, A and B.
Table of Possible Switch Options:
Switch 1: Pickup Split Switch
Switch 2: Series / Parallel Switch
A & B in Series
A & B in Parallel
Comments: It's meant to be intuitive. Everything's in Series when both Pull/Push Switch-Pots are down. You want them in Parallel? Pull the "Series / Parallel" Switch Pot. You want them split? Pull the "Pickup Split" Switch Pot. When the "Series / Parallel" Switch Pot is down, that "Pickup Split" Switch Pot selects Pickup A, your preferred pickup. When the "Series / Parallel" Switch Pot is up, that "Pickup Split" Switch Pot selects Pickup B, the other pickup.
I dream of owning a Goldtop Les Paul, with P90s. At the time of writing, I recently found a Slash Signature Model Epiphone Les Paul Goldtop for sale. That model has humbuckers. I thought, why bother getting a Les Paul with only P90s? I figured I could buy the Slash Signature Model and install P-Rails. P-Rails are Humbuckers made from a P90 and a thin "Rail" coil. They're like P90s with extra "oomph." But no-one wants permanent "oomph." I wanted to choose between between "oomph"-filled P-Rails in Series, "quack"-esque P-Rails in Parallel, the classic P90-only sound, and the single-coil-esque Rail pickup alone. And I wanted the switching to be intuitive. So I thought up this diagram. Then I remembered ChrisK and Yogi B already did binary switching modules; but not the same, as far as I can tell. Anyway, I hated the Slash Signature Model's neck. The diagram can wait for some other time.
To extend this thought a bit farther, with a 3-pickup Strat-ish axe, one could use this wiring for the neck and bridge SCs, giving either alone, or both N and Br in series/parallel. A third P/P pot could then add the middle pickup to the output of the binary tree (or not add it, in the other position), giving N + M, B + M, B + M + N, (B x N) + M. One would not have the middle pup by itself, but probably a majority of Strat users don't use that setting much anyway- this gives them the "quack" settings they use more.
If middle alone is desired, rather than a 3rd P/P, one could use an On-Off-On mini-toggle to either add the middle to the binary tree as above, or to have the middle by itself, or have it off in the middle position of the switch, with just the binary arrangement going to output.
In my case I think context is also important; I'm in the latter camp for normal switches, but the former for push-pulls. Probably because it is easier to switch two toggle/slide switches simultaneously (e.g. to go from series to parallel, or to swap the selected single coil), than it is to pull simultaneously pull two push-pulls.
Steve Hoyland / Jimmy Page / Gibson seem to agree with me on that point, as Gibson's Page number 2 signatures have the pickups' series/parallel operation on the volume pots and coil-split on the tones. (That, however, isn't actually a full binary-switching variation as the coil-split only works in series mode and only ever gives the outer (screw) coil.) (In other words: congratulations asmith you've created four thirds of two thirds of the 'official' PAGE#2 switching!)