I think we have the original toilet...the yellow matches the gel coat inside the trailer except, of course, for what thirty years of use has done to the color. It looks like a tall portapotty.
Apparently, you pump the water into the bowl, do your dooty and then push a lever that opens the flap that lets the contents empty into the collection portion of the toilet. There's no separate waste holding tank..it's part of the toilet.
I've tried to upload a picture of the part that's broken. It's the rubber seal on the pump plunger that is used to bring the water into the toilet.