I hope that this answers your questions.
I originally got this at Camping World but I searched the website and can't find it. I found it here though.
It's red and comes in two pieces.
One piece fits the large hose and the other goes into the sewer hole at the campground.
Here is the cap with hose connector I use at the galley drain.
Make sure you put it on with the hose threads at the 6 o'clock position.
Go to your hardware store and tell them you need a male to male connector for a water hose.
The red sewer connector and the the cap for the galley drain both have male connectors on them.
I also bought a yellow screw on cap to put on the red sewer connector when I need to plug the hole.
I keep both gray valves open all the time (at the camp site).
The last day we are there I close the grey for the shower so that I have some soapy water to rinse the big sewer hose out with after I dump the black tank.
I took the 25' grey water hose and divided it into two pieces.
I usually need about 10' to reach the red connector from the rear galley tank.
I hope all of this makes sense.
I attached a better drawing.
Maybe that will make it clearer.