I was asked my Marshall in a message to try to sleep for longer times. It seems sleep sets a time when it should wake up again and while SIGTSTP does stop the process it does not stop the passing of time. (I am guessing about how sleep works.) If you want different behaviour you have to replace sleep() with something else.

$ perl -E 'for (0..100) { say "$_: ". time %100;sleep 33;}'