First of all, it's not really a good idea to fill your boat with water... there are too many things that can get damaged by being soaked, and often you can't get enough water in the boat to find the problems without drowning parts of the engine.
In your case, it does look like water is leaking past the seal between the gimbal housing and the transom. That often means the transom has become soft from rot. If that is the case, a rebuild is in your future. You can drill some holes (from the inside) into the wood transom core to see what the shavings look like. Use a 1/4" drill bit and make sure to not drill any deeper than 1.5 inches or so, or you might penetrate the outer skin of the hull. If the shavings are wet and/or dark, you have a bad transom.