Thanks for this, @donkeypong.
My neighbor gave me a recipe similar to this recently, with vinegar but absent the dish soap.
I believe your version would work better, as the dish soap would act as a surfactant, essentially making the water "wetter," and thus making it easier to get the active ingredients into the fur and skin, effectively neutralizing the odor
By the way, original scent Dawn dishwashing soap is the best dish soap to use on animals, hands down, as it is what animal rescuers use for everything from stray dogs and cats to oil-covered sea birds and marine mammals. It works, it breaks down oils quickly, and it does not harm their skin, as many detergent-based dish soaps can do.
Make certain that you get original scent Dawn, not a differently scented version, as the latter may have chemicals that would be detrimental to your animal's health.
Thanks again! Hopefully we'll never have to use this recipe.