Thanks for the additional pics!
That aqua & white striped hose is the water filler hose for the fresh water tank. This means your fresh water tank is in the rear of the TT. It also appears that your fresh water tank is below the floor. You didn't say how many are tubes are exiting through the bottom of the rear of the coach, but there should be two for the fresh water tank- one (with a valve) for draining it and one that serves as an overflow/vent. On my 266 FBS, the black holding tank occupies this area as my bathroom is in the rear.
Do you know where your water pump is located? If it's setup similar to the way my water pump is, the hose that gets inserted into the RV anti-freeze jug for pumping it through the water lines should be close by.
According to my 2000 Jayco Eagle Brochure, a water heater bypass kit and winterization kit was standard equipment on all Eagles.
For what it's worth, below is a picture of the water pump, front drain valves, fresh water tank and winterization kit on my 266. You can see a little bit of the "pink stuff" in the clear vinyl hose that gets inserted into the RV anti-freeze bottle. You can also see the aqua & white water filler hose that is connected to the upper corner of the fresh water tank. On my TT, there are three drain hoses exiting in this area. One for the water line, one for the fresh water tank and one for the overflow/vent on the fresh water tank.
At this point, it might be worth a call to Jayco's customer support. I'm sure they can easily provide the definitive answer as to where all your drain valves are and how to gain access them.