The biggest step that can be taken to deal with gray water, is to conserve water in the first place. Big rigs can use a lot of water and that makes dumping gray water an issue, especially if there is a convenient source of water but no dumps.
I do a lot of remote camping and have learned to conserve water. When water and dumps are not available, I get by on about 3 gallons of water a day. That includes a shower, drinking, and washing dishes. Each takes about 1 gallon per day. My gray tank is 15 gallons and I generate about 2 gallons per day. If I have ready access to water, I might back off and use a bit more but I am so used to getting by with little, I still only "waste" another gallon or so a day usually on a longer shower.
I take a couple of other steps in dealing with gray water. First I have a fine mesh screen on the sink drain to minimize food particles in the gray water. Second, I frequently add a small amount of bleach to the waste tank.
With 2-3 gallons of relatively clean gray water a day. Keeping up with emptying the tank is pretty easy. I usually empty the tank before it is half full. My kitchen trash container is a 5 gallon bucket which used to hold kitty litter. It is easy to make a couple of trips with 3-4 gallons in the bucket. Finding a place to dump those relatively small amounts if rarely an issue. Many campgrounds have an area designated for tent campers to dump their waste. If not, absolute worst case, I might need to dump in the bushes somewhere. I try to avoid doing that anywhere near where people actually walk or camp. I suppose dumping in a toilet or outhouse is an option but I usually try to avoid adding the waste volume. Another option is to ask the campground host where you should dump "dishwater".