I don't know terminology, so bear with me here.
The problem is with my 51 and my Tele, but my 51 especially.
When soloing in the realm of the 12th fret on the treble strings, A and low E will vibrate and ring on their own unless I mute them with my thumb. The problem is worst on the 51 to the point of being distracting. Not so bad on the Tele, but still there.
Maybe it's a coincidence, maybe not, but both of the guitars are hardtails, strung through the rear of the bridge. The Jagmaster does not have this problem, and I don't play my strat, so I don't know there.
What are my options for getting rid of this problem, because it's really making me not want to play my 51 at the moment ☹