the dish soap acts as a surfactant, it's harmless (@that dosage), there is an organic equivalent, it's a plant based oil, i actually have one, but it's the dark cycle in there right now and i can't go get it, but i remember it being pretty cheap and a little goes a very, very, very, long way, i've had the bottle for years and i haven't even used a quarter of it (pint sized).
I want to say it's a tropical oil, damnit i can't remember.
It's a transparent oil.
Neem oil doesn't seem to do squat to mites, in my experience anyway.
Not a whole lot that does affect mites, organically anyways.
miticide during vege, turn the plants upside down and dip them in a 5 gallon bucket of the solution, just not flowering plants.
works waaaayyy better than spraying.