For knowing when and how long to take a break, the Pomodoro technique is worth a try. You basically alternate between 25 minute work sessions and 5 minute micro-breaks. The breaks are too short to actually do anything in, just step away from what you're doing (probably on a computer terminal), walk about a bit and space out for a couple of minutes. Start with the default technique, then adjust the intervals to see if something works better.

A lot of my idle time goes to browsing the web, but I do worry occasionally that there's something to Alicorn's experiential pica idea, and browsing vapid stuff is just a self-reinforcing cycle of uselessness.

It might be also useful to separate breaks as switching gears and breaks as rest. Running and concentration-intensive meditation can both require exertion, but they're also quite free of the sort of demanding decision-making you need to do when working, and could be considered rest along that dimension. The exercise aspect will also hopefully boost your physical and mental stamina. I don't know what's the good amount to spend running or meditating though, but at least both activities have reasonably natural session lengths (time to run some familiar route, around 30 minutes meditating), so it's simple to do something like 1 session a day or a few sessions a week, and end up with probably not that bad parameters. (On the other hand, I have a hard time figuring out what kind of bodyweight exercise routine is long enough, so I end up doing nothing at all.)