I just skimmed through an article (from HN, I think, but i can't seem to find it) about using DNA and PCR to find animals in streams that are otherwise very hard to find.
This seems like a perfect tool for diagnosing some of these sufferers. If there is some sort of tick DNA that shows up, say, in the water after a thorough scrubbing in a bath, then there's a good chance that a tick infestation is the actual cause.
The article you're referencing is detection of the notoriously secretive Idaho giant salamander [1]. Your idea is particularly interesting because it has already been used to detect and study the diversity of Demodex face mites in humans [2].
A somewhat disturbing, but perhaps not surprising, fact is that 100% of people studied in the Demodex article had detectable mite populations on their face.
This seems like a perfect tool for diagnosing some of these sufferers. If there is some sort of tick DNA that shows up, say, in the water after a thorough scrubbing in a bath, then there's a good chance that a tick infestation is the actual cause.