if its coming from the rear of the motor then the motor has a missing/dis-lodged core plug or a crack.a water leak from the transom cant jump to the back of the motor. you can hook a hose to the therm housing and close off the manifold and riser hoses and apply water you eliminate the drive from the equasion.
If water leaks from the motor the motor is cracked.
Then apply water to the inlet hose you took off, any leak will be very apparent.
water runs downhill, so start at the bottom and work up.
If you suspect the Y pipe, remove the risers and stick a hose down and turn on the water, water leaking inside the boat is a rotted Y pipe.
If no water leaked then suspect the trim hose plate and gasket
Removing the drive would show water in the main bellow if that was bad, the shift boot can be visually looked at for tears or rips.
the typical setup is the connector fitting coming thru the transom to a PS cooler, to the therm housing, out of the motor to the manifolds and risers.