Early Twin-2’s had aerodynamic elevator trim (trim tab), but later models went with spring trim. The jumping back reminds me of a slipping trim bar where the desired trim position doesn’t hold its setting. Recommend you pull the front seat and see if there is any slipping of the desired trim position. Can’t remember exactly what the trim setup is on the Twin Two, but a look under the seat will reveal any malfunction.
Hope this helps,
JJ