This is an interesting modification to try. I've always thought of this mod as similar to the 1953 telecaster schematic. I had a squeir classic vibe and got to try this out as part of the sales pitch was to have it as close to the 50s wiring and sound as possible. I used Dunlop pure nickel strings to help with it. I ended up using the jazz mod as a push pull and the main tone was a greasebucket tone and the selector was normal. So best of both worlds 50s and now.

I'm no jazz player but this is a cool mod for all guitars. The concept is similar to a varitone but instead of there being 4-6 unique tones it's just one you really like. So with this there is no "right" capacitor value it's preference. Jazz strings like half wounds or chrome strings which are really smooth and super thick picks can help for more of a jazzy tone.

this mod can be done two easier ways then re-wiring a guitar. We want this simple.
with a push pull pot
or the appropriate mini toggle.

parts needed
one 0.1uf capacitor. Or two 0.047 capacitors in parallel is close enough to 0.1uf
other than that nothing fancy

here's the schematic