I put a cap of LIQUID automatic dishwasher detergent down one of my sink drains once a month, rinse with a small amount of water and let stand overnight (I rotate thru the shower, bathroom sink and kitchen sink so one is done every 3 months). I really don't do it for the grey tank so much as I do it for the drains and p-traps. It helps to keep the soap build up down. I have very, very hard water and even though we only use liquid soaps, it still has a little buildup. I also clean my toilet (residential) with the same dishwasher detergent.
The same is done for my daughter's truck camper. She has a standard RV toilet.
We just don't really buy much in the way of specialty cleaners. And most "RV" labeled stuff is an overpriced marketing gimmick. My concentrated liquid hand dishwashing detergent is diluted and used to hand wash some dishes (what doesn't fit in the dishwasher), diluted and used as hand soap, added to my vinegar & water solution for floor mopping and most hard surface cleaning, and used, undiluted, to wash all our clothes. And I don't use Dawn at all. It uses one of the fragrances that I'm allergic to.