| Sulu,
Try muting the strings behind where you have them fretted, towards the nut. As onlyclave mentioned, when you're fretting up high on the neck, the string can vibrate on both sides of the place you've fretted--from the nut to the 11th fret as well as from the 12th fret to the bridge when you're fretting on the 12th fret, for instance--and that "backside" portion of the string will generally be out of tune with the other half. There can also be sympathetic vibrations from other strings, which can be out of tune as well.
Another possibility is that the pickups are high enough to interfere with the string's vibration when you're fretting up high, and that can sometimes make the tone sound "wobbly".
Finally, you may just have a high fret up high on the neck that's buzzing a little bit. Hard to be sure exactly what you're hearing when you say "twittery".
Mike
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