Wonder if there is a good rule of thumb to keep working on the system if there is a lot of time between support requests. Like writing additional tests, interference testing to find patterns of failure and so on to move to deeper understand it.
Testing is also good, if it's testable. Based on your description, I'm guessing it isn't very testable. Testing and refactoring together is a good cycle.
Setting up a repeatable environment is huge help. Build/test should run on every commit in CI. Dockerize it if it isn't already. Have as many official environments as you see fit. At least a dev that is kept up-to-date and production, of course.