The glass in that area is probably less that a quarter inch thick. I noticed on my Islander a flex in the transom for the same reason. When I remounted the outboard mount on my Islander I used a piece of starboard the length of the inside area where the mount would be connected and added a support at the top inside the deck and bottom on the inside hull. I shaped the starboard to fit flush and glassed it in. Maybe overkill but it cured the problem and I felt much more comfortable. I used starboard because i only wanted to do it once.
A people that values its privileges above it's principles will soon lose both.