Quite a few light aircraft horizontal tails vibrate or oscillate a bit in flight - just don't look back if you are flying a Super Cub or a Pawnee for example ! The tails may be wire braced but they still vibrate.
The Grob 109's horizontal tail also shows light oscillation occasionally in cruising flight, and more evidently when flying engine off, presumably because of the turbulence off the stopped prop or perhaps off the cockpit area with the change in airflow. T tails will accentuate these - ho0efully small - motions because of the moment arm.
I hope that is some reassurance, though I did think the last Tomahawk I flew felt a bit 'squirrely', perhaps because of that.
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