Being on-call is mostly boring work. It's just waiting for something to happen. Good thing is that you are not tied by the work. You just need to be able to step up and start working any moment. So it's a good thing when nothing happens and it gets boring. You have a lot of time to do other things. Things that might otherwise not get done.
While waiting for something to happen you can't really do anything that requires deep concentration or a lot of uninterrupted time. But it's a good time to do those those menial tasks you have been putting of for way too long. Things so boring that you wouldn't want to do them any other time. It's still better than just waiting for something to happen. It changes that fear of something happening to a hope. You start to wish that something goes wrong so you wouldn't need to do whatever you were doing and instead start solving the issues whatever disturbed you from your task.
Maybe this is one of those tasks now. Luckily I didn't get interrupted while writing this. But I had to get this done as I still got one more hour to go.