The "transom assembly" is actually the Bell (Gimbal) Housing Assembly.
The Gimbal Housing assembly has rubber components (bellows) that can rot and/or rip and leak.
The two rubber components most likely to cause a water leaking into the baot are the Ujoint Bellows and the Shift Cable Bellows.

Replacing the Shift Cable Bellows requires removal of the drive and replacement of the shift cable.

Leaking U-joint bellows will cause severe damage if not tended to immediately. Not to mention the boat possibly sinking.

The two most common symptoms noticed first by customers are water constantly leaking into the boat
and noise coming from the back of the engine/drive area. It's important to note that once these things are noticed, that some damage has already occurred.
The grumbling noise that so many customers hear is from a rusted gimbal bearing. The noise will get worse as the drive is turned to full left and full right.
Sometimes a customer will notice water in the drive lube as well. The front seal of the outdrive is meant to hold OIL in the drive and is NOT meant to hold water out of the drive.

Inspect the Gimbal Housing Assembly:
With the boat out of the water, take a good look at the bellows with the drive placed in different positions.
Look for barnacle growth, rips and deterioration of the rubber. The bellows should be clean and firm
A complete inspection will require the removal of the outdrive.

The rubber bellows should be replaced about every five years or sooner if you suspect a leak.