I worked on volatility control funds for a few years a while back. Frequently, we would simply use the average as the threshold between high and low vol. That is because volatility is below average in normal times, but can quickly exceed the average during a correction. Mathematically, the fat right tail of an inverse-gamma distribution for an unknown variance makes the average greater than the median/mode.
How an institutional investor perceives risk is another matter. They are looking at their portfolio risk, so you want portfolio volatility. You probably can’t just use S&P 500 implied vols. If you are testing the reaction of investors to realized vol, then you can just do a 21-day moving average realized vol or some backward-looking measure. It may be beneficial to start there, see if it’s significant. Otherwise, the next step may be to estimate vol using a GARCH model to better capture the persistence of realized vol in the future.
Your experiment feels like research more than practical application, so whatever you choose, be sure to justify it.