Re: POLL: Most Important Factor in the "Tone" of an Electric Guitar?
Where do we factor in the body shape? Ever thought about the reasons why they look like they do? (It's not all tone, it's not all practicallity)
And just for ease I assumed that we are talking non-chambered, solid wood electric guitars right?
Of course pickups are first, as any self-respecting guitar player should vote

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Then the gray area starts. First we can distinguish the influence before and after the pickup, i.e. electronics and 'the guitar itself'. Arguably electronics are the most influenctial in the gray area, especially when you go with 1k pots and 1u caps or something crazy electronic wise, so that one is second to me, because that is the area we can still mess it all up and can hear some relatively big differences (to verify the influence of your electronics, just wire a pickup straight to your jack). BTW When 'pickup placement would have been possible it would have been my second choice0. Just listen to the difference in neck and bridge pickups and everything in between those to positions, that is a dead giveaway runner up.
Then we come to 'the guitar itself part'. As someone who has their master in applied physics I find it rather difficult to single out one factor that is most important here. In the end you pick up string vibration, and what they see first is the nut/fret and bridge as end points. Yet they do not have to much mass to them and therefore are not such a great 'basin' for tone. They do have their influence and coloration. Also the way they transfer the energy from the strings to the bridge/nut/fret will alter the tone and then how the transfer from the bridge to the body and the nut/frets to the neck goes will have an impact (maybe small, but still).
Then we have the woods, the biggest wooden part, therefore the biggest 'tone basin' is the body wood. But then there a lots of things that make a wooden piece sound the way it does, first of all its density, its shape (height, width, thickness, curvatures etc.), yet also the way its surface is terminated (the finishing process), how much of it is cut out for electronics etc. the shape of those cut outs, the influence of this stuff is small, yet theoretically sure is there...
What goes for the body wood, of course also goes for the neck wood, same arguments go for wood (density, shape etc.), yet here we also have the fretboard being added to the equation. and the joint with the body.
Yet in phyisics an important theme is transfer of energy, which is also crucial to me in guitars, the way you strings are connected to your bridge, and the bridges to the wood, the woods to each other. In physics really in the transfer of energy things change. Therefore my third choice was the construction, the way and quality of the joints. They may not be the major makers of the sounds, yet in its transportation they are major players.
And the honorable mention goes to the strings. They make up a really big part of the sound, yet since there is so little variation available (and reasonably so) you really cannot chance a lot by changing strings, you might add a little emphasis here or there, maybe some sustain or volume, yet big changes cannot really be made. If that would have been the case, strings would have been my second choice, after pickups.