This post is going to be a bit anal,

I hope the OP and all the other good folks in here won't mind.
I have noticed over time that the question "how do I approach playing the Hammond" is often addressed with an emphasis on things like adjusting your playing to non weighted keys, learning how drawbars work to shape the tone, the use of percussion, chorus/vibrato, when to switch the Leslie speed, and so on. Books like Dave Limina's and Brian Charette's follow more or less this approach (by the way, there is very little teaching material around about the Hammond in general).
Nothing wrong with teaching those things, but it seems to me that this ignores the "elephant in the room" question so to speak, that is the music itself. The ever-present (and valid) advice of "just learn from the masters", while always true for any instrument and genre, might not work so well when one is at the beginning of his journey, which is where I'm assuming the OP is at at this moment.
So here's when I'll get anal.

The organ (be it pipe or electric) is an instrument with unique features:
1. The ADSR envelope (to borrow from the synth world) consists of a sudden attack, an infinitely flat D-S, and zero release.
2. No key dynamics/velocity affects anything in terms of volume.
3. Expression/volume is controlled (on electric organs, less so in pipe organs) with a pedal that affects every note, whether that's already being played or not.
Apart from synthesizers, which can be programmed to behave any way you want, I'm not aware of any other "natural"/acoustic instrument which possesses the above features all at once.
But this is not just an academic arguing for its own sake. These features demand and even impose a very different playing approach and even
mindset from any other keyboard instrument's. All of the above is going to have a big effect on things like chord voicings above all (how many notes, which ones, how wide/close...), or even whether and when to use chords at all, and it's going to make all keyboard approaches, that in order to sound good rely heavily on the sustain pedal and/or on key dynamics, pretty much unworkable on the organ. Anyone who's ever tried to play a digital piano without any sustain and with dynamics disabled will certainly have noticed immediately how much music doesn't all of a sudden sound good at all.
Figuring out what to play and how to play it is, in my opinion, much more "the point" than learning when to switch the Leslie on fast and things like this. It's about finding one's own voice with an instrument that, despite looking like a keyboard instrument like many others, has to be reasoned through totally differently.
I'm mainly talking about jazz here, which is the OP's concern. In organ jazz, there seems to exist this unspoken rule that says that in order to play organ jazz, you'll have to 1) play left hand bass with an 848 registration, 2) play solo lines with the 888 registration and percussion on, with a lot of cliche lines, 3) occasionally squabble as opposed to soloing, 4) have a guitarist in the trio to fill in the harmony (with a clean tone), and alternate solos with, 5) be as groovy, bluesy and funky as you can. This is the Jimmy Smith school which has become "the norm", when in fact it is just
one possible way to go about it. Yet, almost every organ jazz players that have followed fall more or less into this style, and the (very scarce) teaching materials that are around just
assume and take for granted that this is
the way to play Hammond jazz. It's as if I wanted to play jazz piano and was taught the stride technique because, well, that's
the way to play piano.
I believe all of this is very unfortunate, especially considering how beautiful and expressive the Hammond sound can be. It can be funky for sure, but it can also be very profound and moving. I'm still waiting for someone to put a Bill Evans-kind-of emotionality in Hammond music. Maybe Rhoda Scott has in certain occasions, and (occasionally) Lonnie Smith. But I can't name many others. In another life, in which I'm much younger and talented, that's what I would be striving to achieve, artistically

. Anyway it's a huge void in organ jazz music, and jazz music, and music in general, that I'd like to see filled eventually.
Gospel players, on the other hand, are a lot more variegated and sophisticated with what they do, and, lo and behold, they don't always use that damned 888-with-percussion registration, and they play proper pedals too. I think there's a lot to learn from them!
Not sure all of this is still within the OP's scope of interest by the way, but I hope it wasn't too far away either.