Tone caps seem to be simultaneously a beaten dead horse and a red flag signal on the Web. I remember an engineer summing up the question by telling me: "Too much noise, not enough signal". How true! So many predefined and non documented opinions promoted as facts...
When I've tried to create a thread about tone caps on the previous music-electronics forum, members and mods even appeared to believe that I was trolling. So I've stopped to post in my own topic (!).
All that being said: lab tests have been done here to understand why some players were hearing a difference between tone caps.
A few leaky capacitors affected the resonant peaks in a different way, not announced by their carefully measured value (there's a life for leaky caps in guitars: they behave like the Fender Grease Bucket circuit, which was probably inspired by leaky caps anyway).
ALL "normal" (non leaky) capacitors were setting the resonant frequency as expected when the tone control was at 0/10: empirical measurements were strictly agreeing with resonance as calculated from components capacitance and pickup inductance. No surprise here.
BUT some differences did effectively appear when the tone pot was "in between" - IOW: set low enough to stop to be purely resistive.
These difference were about harmonics with a same pickup excited by a same electrical stimulus: harmonic spectra stacked exacly upon each others with some caps of the same value. With other caps, they had a different shape.
It happened with caps of different AND of the "same" materials (harmonic differences were noticed with mylar caps of various origins, for instance). It was NOT a random error due to the testing rig. There WERE repeatable differences - and in fact, I've already shared a few graphs borrowed to the related data, here on the Duncan forum, a few years ago.
I've never heard of similar tests done elsewhere than here.
Even if I was in situation to share the related data, publishing 'em wouldn't necessarily make much sense since people trust only what they do and notice by themselves.
So let's leave here the principle of such tests: one has to use an electrical stimulus producing a fundamental and its harmonics, injected in a guitar pickup. Consistency of the harmonic spectrum must be double or triple checked with a resistor instead of a tone control and without any capacitor to start with. Then capacitors can be inserted between "tone resistor" and ground. A few dozens of tests should suffice to illustrate what I've explained above.