Your transmission should be a Hurth v-drive.
Just pull the intake hose off the lower end of the transmission cooler. That will drain it. You probably already did that when you pulled the hose off the raw water pump. There is no water that circulates through the transmission. The hoses you're seeing attached to the transmission and cooler circulate 15w40 transmission fluid through the transmission cooler.
'04 MariStar 230VRS/MCX