Well, since I'm retiring in 6 weeks, I'm hoping we can visit a friend in Portland next season and hike with him. Maybe I'll get a chance to try the stuff against your mosquitoes.

I do know that my old non-DEET choice, Bite Blocker, which was rated less effective than lemon eucalyptus, worked fine in SE Alaska about 10 years ago when I was there in summer. Those are the only two "herbal" type repellents that have ever worked at all for me, but they've both been pretty good. Bite Blocker is a little thicker and tends to gum up its spray bottle, but smells less obnoxious (kind of vanilla spice-y) and might even be non-toxic for pets, not sure (active ingredient is actually some sort of modified soy oil). I would not put the lemon eucalyptus on a pet, for sure.

I saw something in my local drugstore a while back that was similar to an air freshener cage, you put refills into it and are supposed to wear the thing to keep mosquitoes away. If it works, it might be something you could hang off a dog's collar. Don't remember what it was called, though.
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dk