Note to Erica: I agree about avoiding the more toxic insecticides/acaricides, regardless of whether they're from natural sources (some of the most toxic substances ever discovered are from natural sources - ricin, for example, or saxitoxin).
Definitely, just because it's naturally derived doesn't mean it's not harmful.
But it's generally a mistake to conclude things like "garlic works by being high in sulfur." This is a common error among many who comment or question on BYC.
Why do you conclude this is a mistake?
Personally, I disagree with this statement, no offense intended. The sulfur levels a chook can tolerate without harm are far beyond the sulfur levels their parasites can tolerate, with the possible exception of very large tapeworm. What's a healthy level for any animal is repellant to parasites, and raising it quite a bit, e.g. doubling or trebling it, while being still well within safe levels for the host, can kill its parasites. But in Australia at least, almost all humans and animals are often disastrously low in sulfur, complete with all the attendant diseases and parasite infestation that allows.
Low sulfur levels are always correlated with an increase in almost all types of parasites and diseases, and raising sulfur levels can eradicate parasites, fungal and bacterial diseases, and more. Doesn't matter if you're talking about soil, plants, animals, or humans there.
I feed garlic to control external parasites like mites, and it works quite rapidly, and it's not the other compounds in garlic doing it. Other sources of sulfur work the same. The sulfur works the same way externally as internally when it comes to applying it to insects, more or less, but since I've never applied it externally I can't vouch for how fast or efficiently it works that way. I hear it works, but I've never needed to use it that way.
Regarding cattle, they can easily overdose on sulfur, so one should be careful adding it to their feeds in neat form. Premixed additives are generally a lot safer than adding straight sulfur to anything's food.
Best wishes.