Yah, I was thinking the same thing, but for different reasons, power washer and a back up water source, my gray fills up ..
Looking like getting a plastic water tank, found what I think will work, a vertical tall one at ~120 gal.. I was also looking at a flat one for a buggy trailer, hopefully in the near future, that the buggy could just drive over.
They might have something here that might help or just search rv water tank or plastic water tank and something should popup that might work keeping in mind, water is heavy.
To fill, just like you fill your camper water tank, hose. to run, like you said, gravity or a small pump like your camper has, surflow..
They have some in a little pelican case, expensive but portable. Also look at Underwater/Pond tanks, pump works when underwater or wet...
https://www.tank-mart.com/plastic-tanks/plastic-water-tanks.html?dir=asc&order=gallons
hope that helps..