> In thinking about the mode of action of thymol, I wonder if it is more repellent than deadly

I believe you are mistaken. The compounds which are most effective in controlling varroa -- kill them. Many studies have shown this, here is one:

> Essential oils and other natural compounds were evaluated for their toxicity to the parasitic mite Varroa destructor ... Results showed that menthol, clove oil, origanum oil, and thymol were the most toxic products, causing 87, 96, 100, and 100% mite mortality, respectively, at a dose of 0.75 mg/vial. 

> Tau-fluvalinate used as a control was significantly less toxic to mites and equally or more toxic to workers and larvae than the above four natural compounds. Results of this study suggest that besides thymol, which is already a registered varroacide, origanum oil, clove oil, and menthol, are potential candidate products to be further tested for the control of V. destructor.

Gashout, H. A., & Guzmán-Novoa, E. (2009). Acute toxicity of essential oils and other natural compounds to the parasitic mite, Varroa destructor, and to larval and adult worker honey bees (Apis mellifera L.). Journal of apicultural research, 48(4), 263-269.

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