I used to get a little ringing above the nut on my Jag, but that was `cause I use a roller nut. Lowering the string trees made it go away.
Is your vibrato balanced and adjusted, or do you tighten it down and use it hardtail? Mabe something in there rings? There`s also a thing called "string excursion" where the string rattles around in it's notch in the saddle. Sometimes Jazzmaster/Jaguar bridges can be maddening if you try to clean everything up completely- so many variables in the setup. Things like string guages, the height of your action, and even how old the strings are, or how long they've been on the guitar, can be signifigant.
Does your ring amplify- do the pickups "hear"it?
What ARE those saddles made of, anyway?
Is your truss rod adjusted propery? I once got a strange sympathetic ring, or buzz, every time I played a "G" note- not just the open G string, but any G. It turned out, that, though my guitar`s neck was acceptably straight, without excessive relief, the truss rod nut was totally loose, and the truss rod itself was vibrating in it's channel. A little tightening did the trick, and while my action was pretty good before, it got even better.
Listen carefully when the thing rings, and see if you can hear what's actually ringing. it`s probably something that's easy to fix, after all.
