After upgrading to Hazel 2.3.6 its Status under the System Preferences Info tab claimed to be stopped even though it was running and the Start/Stop button was dysfunctional. Toggling Start/Stop Hazel with the menu bar icon worked, and temporarily fixed the Info tab Status (but not the Start/Stop button behavior).
Not the clearest explanation but the point is that the Info tab's start/stop functionality and status reporting was confused after updating, That worked again normally, and correctly correlated with menu bar actions/status, after the system was restarted.