Hi there,
Did you ever solve this problem?
I have the same problem and for me it is most evident while quietly finger-picking on the acoustic and rockabilly models.
It is definitely since v2 as I have tried going back and forward between 1.9 and 2 and it is not there in 1.9.
I have seen it on a couple of jtv59p models (they are the only ones I have played).
It is completely different to piezo quack, it is more of a static sound as you describe.
I have noticed it is not there when using a plectrum, just my fingers, especially my thumb. Makes me wonder if it is a ground/electrical problem? (Complete guess).
Considering returning the guitar and giving up as it is very annoying, and like you I am vey surprised not many people have complained.
Thanks,