The coil tap affects all the pickups. When you pull the tap and put the pickup selector in the middle position, you get this awesome sound that's hard to describe - it has characteristics of a lot of different guitars, a tele-like shimmer, LP-like bell tone. It's really it's own kind of instrument and it's very versatile. Lessee,
(three pickup positions) X (four knob toggle combinations) X (at least a half dozen reasonably different volume and tone knob combinations) X (any number of effects)
= a tweakers dream of different tones!
As for pulling off the different musical styles you mention, that's really up to you. It's not gonna replace a semi-hollow for jazz tones, but there's more than one way to define jazz. The only way to really know if a guitar is right for you is to really spend some time with it (unfortunately). It took a long time for the JS
to warm up to me, perhaps because I got mine new and it still thought it was a tree, but it's always been my experience that the break-in period is for both guitar *and* owner.