I use a white hose for fresh water and a gray hose for flushing. I don't like the Y connection idea. Check valves do fail...It takes 10 seconds to disconnect one hose and connect the other. All right, it might take 20 seconds.
I don't agree that you need the black tank 1/4 full after flushing. With my toilet all I have to do is hold down the foot pedal for a few seconds to fill the toilet bowl which I then dump. It wouldn't hurt to add a second bowl full. I don't know if that is equivalent to 1/4 full or not but seems to work well for us.
