G'day Rob,
What you're experiencing on your guitar is not unique. If you check other guitars chances are you'll detect sympathetic resonance on them too. All my classical guitars vibrate sympathetically just as you describe. The steel string acoustics don't. As well, the classicals have a sympathetic vibration on the E string when the seventh fret on the A string is plucked.
It doesn't bother me because I don't have a pickup amplifying the sound. But now I'm curious to know why ... let's wait for superior knowledge to give us an answer.
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