I spent almost an hour digging around for an article, but my Google-fu left much to be desired. I saw a paper a few months ago (granted, I think it was much older than that) measuring the resistance of an air (not vacuum) gap. Spoiler alert: it was very high.
Considering that conductance through a vacuum is likely to be due mostly to thermionic emission, there's going to be a very strong dependence on temperature for that one. I wonder if you could get a back-of-the-envelope calculation of the resistance of vacuum at room temperature by extrapolating a filament current vs. plate current curve for a vacuum diode.