Pinch harmonics aren't random, you should be able to get one 100% of the time you try, and never when you don't.

A hotter pickup and more gain will make them more prominent
"what are good intermediate classic rock covers?"
Quote by EZLN libertad
alice in chains, stone temple pilots, led zeppelin, play rock and roll by zeppelin, thatll work well, maybe hendrix
and maybe war by meshuggah

It's a bit more complicated then all of that. More windings add to the harmonics but different types of magnets do as well. Alnico magnets give better pinch harmonics than ceramic. Alnico 3 are better than alnico 2 and alnico 2 is better than alnico 5. Small magnet alnico 5 gives you brighter clearer harmonics but large magnet alnico 5 gives you louder harmonics. There are also factors such as how tight the pickup was wound, the type of potting, if the pickup has a cover, and what type of cover it has.

Basically, the more metal you jam into the pickup the more harmonics it'll have. The metal can be in the form of covers, magnets, or wire. Some types of metal add more harmonics than others. Sometimes adding metal will give you more output (like when you add windngs to the pickup in order to make them high output) and sometimes the metal will lower the output (like adding a cover or usings alnico instead of ceramic magnets)
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Pinch harmonics aren't random. You can hear them with the guitar not plugged into the amp, as long as you hit them right, just like with natural harmonics.
^but some pickups will amplify them better making even the sloppiest harmonics sound like you hit it bang on.
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i think active pickups are more "likely" than passive ones.
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