I've considered the same issue from the point of view of boondocking and wanting to dump grey water without running it through the black tank dump...and contaminating it. If I dump grey water in a bucket, I can water trees with it....assuming the situation allows for it. And in CO, with our severe water shortages, grey water is great for irrigation.
(This has been debated to death, so find those threads elsewhere.) Anyway, I won't do it if it's been contaminated by a filthy black tank dump exit.
You might consider putting a "Y" in the grey tank dump line upstream of where the grey and black join together. Previous responses may have touched on this already. Frequently the grey plumbing is 1 1/2", and it's easy to install an inch-and-a-half dump valve in a convenient location at the end of the "Y". This option leaves your grey water connected to the black tank dump so you can flush your stinky slinky with dishwater.
If you discover you have problems trying to add fittings in a rigid 1 1/2" line, Fernco fittings will solve that problem. You can even use a Fernco "Y".
https://www.supplyhouse.com/Fernco-Q...iABEgLAqfD_BwE
Fernco fittings come in all shapes and sizes, so rather than a 90 degree "T", you might want a 45 degree "Y". Home Depot carries the stuff.
These are soft rubber drain plumbing connections that enable you to add fittings anywhere in a rigid line. Add a short section of rigid pipe and the dump valve, and you're in business. They are also good for relieving stress from road vibrations in long rigid drain lines. I had one crack at a "T", so I replaced the cracked ABS T with a Fernco, and now there's a bit of give in the line that can absorb road shock and not break.
One more advantage of a clean, separate grey tank dump. I park my PUP, open the grey tank dump, and use a garden hose in a sink drain to flush out the grey tank. There's never any residue in my grey tank, and with a clean exit, I have no qualms about letting the grey water run out onto the ground next to my driveway.