What does ATC do during "slow" times?
Admin stuff, emails, chat with a colleague if you are not alone on shift, read up on (ever changing) procedures, eat, read a book, make sure the coffee machine works, meditate, watch TV. Anything goes, really, as long as you keep an eye on the radar and stay close enough to hear the radio and answer the phone. Of course, this is all assuming that there are literally no aircraft in the sector at that time (which happens regularily at smaller airports). Whenever you have any active aircraft, you obviously need to stay quite focused on that.