The first thing I looked up was the "active ingredients" in Listerine. My search showed me eucalyptol, menthol, methyl salicylate, and thymol was what made Listerine work. I already knew some of the plants/phytochemicals had anti-bacterial qualities, but didn't know why they would work for wool mites.
First of the one I was most familiar with Thymol. I looked up Activities of a chosen chemical.
Among activities listed for it were : Antibacterial, Antiseptic, Fungicide, Insecticide, Insectifuge, Nematicide, Pesticide, and Vermicide. That means it not only is an anti-fungal and antiseptic, it has actions against worms and pests. That was good news for a safe ingredient.
Next on the list is eucalyptol. Activities: Antiseptic, Insectifuge, Pesticide, and Vermicide.
Then was Menthol. Activities: Antidandruff, Antiseptic, Pesticide.
Hmm... I was beginning to see why this "home remedy" might have some potential!
I decided to check out the synergistic properties of those three chemicals together. (Synergistic is when the chemicals work together so that the total effect is greater than the sum of them individually working) Sure enough when I entered the items in it showed heightened activities for insecticide for those chemicals together.
So, I can see where it might be a viable option for a case of mite that wasn't extreme. I have heard you can dab the listerine on, or use a small spray bottle. I would think you would need to get it down to the skin level and I don't think I would want to get one completely wet from it. I can't recommend whether to use dilute or full strength, as I have not yet tried this remedy. I WOULD be careful to choose a variety of Listerine that does NOT contain fluoride.
Let me know if you try it and how well it works for you!