The hollow body is, I believe, an Anniversary Deluxe, judging from the avocado motif. I don't know what they've done for pickup switching. What used to be the tone switch in a regular Gretsch wiring scheme looks like a push-push switch now. And then there is an extra toggle switch just north of the Bigsby at the tail end of the guitar. I have no idea how all of that is supposed to work.
The solid body is called a Gretsch Triple Jet, though there may still be only one of them in existence. Jack White had it made to his specs. It looks like there is an off/on switch for each pickup. But there is a toggle on the top bout, too. And three knobs. What I would have done, limited to that topography, is put three volume controls, one for each pickup, and I would have made the top bout switch a Gretsch-style tone switch. That would not be very much different from my Zephyr Blues Deluxe which has individual volume controls and a master tone control.
The problem with the ZBD is that, while there is an infinite number of tone variations possible (some of them even interesting), zeroing in on one takes a minute or two. A minute or two that is going throw your live performance right in the twahlett (as they say in the south of France). Even going from your neck pickup to your bridge pickup involves turning the volume of the neck pickup all the way down and the bridge pickup all the way up, something that takes a couple of seconds to do. If you watch somebody who switches pickups a lot, like Stevie Ray Vaughn for instance, he does it so fast that most of the time you can't even see it. That's probably what the three switches are for on the Triple Jet: some way to change pickups quick without diddling the volume controls.
I have actually made something of a study of this. There have been two dominant setups over the years: two pickups with a neck-both-bridge switch and three pickups with a selector switch. At first the selector switch on a three-pickup model just selected neck-middle-bridge. I believe it was Jimi Hendrix (but there might have been others) who discovered that putting the switch on a Stratocaster between the detented positions gave you neck-plus-middle or bridge-plus-middle. These other tones are kind of hollow, but tonally very interesting on cleaner non-overdriven stuff. Mark Knopfler, the Dire Straits guy, used them a lot. Because the switch doesn't want to stay in these intermediate positions (it keeps wanting to flop into one or the other of the detents), people started putting five-position switches on Strats that gave you detented positions for all five tones and now they are totally standard--you can't buy a Strat without it.
What the five-position switch doesn't give you is the neck and bridge pickups together. Or all three pickups at once. The neck and bridge combination is another of those "interesting" tones that is distinct from the other two-pickup combinations due to the fact that the active pickups are farther apart. Danelectro in its reissue incarnation was the only group I was aware of that tried to give you all seven pickup permutations in one instrument. On several of their three-pickup models they put a six-position rotary switch which gave you all but the all-three-together tone. Then they added a separate "blow switch" that put all three pickups in series irrespective of the current position of the six-position selector switch. Because all of the pickups are in series with the blow switch on, mostly what you get is LOUD, which is probably why they called it a "blow switch." I never thought the all-three-pickups-at-once combo was interesting enough to pay money for until I bought the ZBD. With all three of its fat-ass P90s on in parallel, it has a really strange hollow almost acoustic tone which can be bent in many different ways by dropping one or the other of the pickups down a bit with its individual volume control.
So now I have come to the conclusion that the ultimate setup is three pickups with all seven permutations available. That, as I have alluded to above, however, poses the problem of how you switch between all of these combinations with an alacrity worthy of live performance. The Danelectro scheme is a mess. The controls are too close together and the six-position rotary switch is not that easy to switch quickly. I drew up a pickup switching scheme years ago that I called the Tallahatchie Tone-Boy wiring system (Tallahatchie because it began with a T). It not only gave you all of the pickup permutations, but allowed you to put the pickups in series or parallel and in or out of phase with each other. This is an absurdly complicated thing to wire up and would be almost as complicated to use. It would really be more of a development platform than anything else: a guitar on which you could wire your pickups in any combination you could think of using switches on the top. You'd never have to switch guitars again. You'd just have to remember which combinations of the eight switches made it sound like Strat and which combinations made it into a Les Paul. This is what happens when engineers get hold of things: incomprehensible features that nobody asked for.
"But what would be useful and usable?" you ask. Nowadays I'm thinking what you need is a linear five-position switch, like on a Strat, to give you the N-NM-M-MB-B switching function and then a three-position rotary switch that would give you the NB combo, the NMB combo or the current position of the five-position selector. The five-position switch would be usable enough by itself, as born out by the hundreds of thousands of guitars out there that have only a five-position selector, but then you'd have these two other options as well. If you wanted to switch between single-coil and humbucking pickups or between TV Jones Classics and Seymour Duncan Head Splitters, well, you'd just have to have more than one guitar, which any working musician is going to have anyway.
And then there's Brian Setzer. An honest-to-god working musician with record albums and multiple bands and everything whose guitars have a three-position pickup selector and a volume control. Period. He never used all of that other folderol so he had Gretsch just leave it off. So there's some perspective on just how necessary all of this musing is.
I still think I'll take one of my $300-or-less models and wire it up this way and see if it's revolutionary or just stupid.