The best way to to get them is to understand how they work and then to practice the technique.
There are high pitched harmonics right under your picking hand as you play. The secret to getting them is to get the skin on the side of your thumb (picking hand) to briefly graze the string as you pick the note. Make sure no part of your hand is touching the string after you pick as this will mute it.
A good place to start is by fingering the 9th fret of the G string. Practice this technique as move around a little bit to find the best spot.
Sometimes referred to as "squealies".
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