if you were to begin a Jimi Hendrix tribute band and you want to do this...
Is there any specific mechanics or techniques you need to master to be able to play like that?
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I wouldn't call that a "master" technique. It's a stage gimmick!
Hold the guitar up so the strings across the body are facing your face.
Push your face into the strings.
The flesh of your lips will mute all the strings.
Part your mouth a bit until you get your top teeth on a string. It isn't too hard to select a particular string, because you're facing the strings initially and your lips are very sensitive to feel the other strings. In a way it's like finding the holes with your mouth on a harmonica.
Your teeth and neck are actual strong compared with your fingers so you don't need to use much force to pluck the string. Sort of push down and back with mostly a neck motion. Pull back enough let the string ring.
For actual performance in front of an audience I would insert the tongue firmly in cheek! :-)
Rubber soles and a separate GFCI (RCD) on the power socket board for your amp seem to be the most important considerations for learning this technique with a view towards being able to showcase it alive.
Also, don't touch any microphone, microphone stand or boompole or parts of the stage or other performer while doing this kind of thing.
Electricity can kill. Giving it access to your mouth makes its work so much easier that it's a good idea to spend some thought on this angle of the equation.