Pinch Harmonics are generated by the very high-frequency wave vibrations of each string. A high-output humbucker would definitely produce a much more "obvious" and louder sound that a mid-output single coil.
Also, as mentioned above, the position of the pickup would also affect the harmonics, being louder and clearer at the bridge, etc.
Turning the tone all the way down cuts down the treble, presence and a bit of mid on the sound, thus, stopping the sound of the pinch harmonic from sounding. Boosting the distortion or turning the gain up would allow the harmonic sounds and frequencies to be picked up more easily.