What makes sense? Don't be discouraged by all those people (like my dear wife) who reckon not being able to play the jew's harp is a service to the rest of humanity.
I recall finding the trick. Apart from getting teeth and things out of the way of the vibrating bit, I have to think about lowering my soft palate to open access between the back of my mouth and nose. What? I just tried it. If I try and breath through my nose - no sound. If i breath through my mouth when I play - bingo!
I drive my tongue back and forth to change pitch (a bit!).
Also! I just remember that I tried a few jaw harps without much success before I got a small one with a little tongue. With this one I can make a really big sound. The others I've thrown away.