Greetings!
While gravity is great to create running water, I’m more a believer of keeping the center of gravity as low as possible in vehicles.
I carry 2 portable 7 gallon jugs of water, usually filled for free from a spigot at the bottom of many drinking fountains.
Rather than running water for my sinks, I find trigger spray bottles from dollar stores to be much handier, and much more water conservative as well. I use several, in one I add a couple drops of dish soap, another is plain water, and a 3rd is vinegar for the really tough to clean stuff, or as a disinfectant, or even as a defense spray. My sink water can be heated by simply placing by window in the sun. I just use dollar store dish pans for sinks, which makes my entire kitchen portable so I can also use everything outside without duplication.
With trigger spray bottles, there is also force behind the water, much more than with a gravity feed system or a normal faucet. They allow for anything from a squirt gun type stream to a forceful spray, to a fine mist. Very versatile. The one with the dish soap can even bring down flying insects.
For showers, or even washing my van, I use a weed sprayer with the wand replaced with a kitchen sink sprayer with a trigger. Once again very frugal on water usage, while remaining quite handy to use, portable, and requiring no power. This also gives me an indoor or outdoor shower without duplication.
Cheers!