You must leave the game unpaused, but you can turn it off by exiting the game.

Emri, I have two seperate games running all the time now. One on my normal user name and one on a separate user name. I am not currently working and am home all the time, so the user name I use the most has my peeps that are set so it's daytime for them when it's daytime for me.

If I can't sleep, I switch to the other username and those peeps are set so that when it's nighttime for me, it's daytime for them. When I play them, they are always full of energy too, but that's because I don't switch to that user name until it's at least 5:30 or 6:00 in the evening where I live -- which is 5:30 or 6:00 in the morning for them and they are just waking up from a good "nights" rest in a game that was not opened all day long.

So, switching their hours around really depends on how you use the game. But they do become well rested even if you switch their hours as long as you're not opening that game up during your daytime.