The question was can there ever be "zero time". My answer to that question was I believe that the only way there could ever be "zero time" is if there was 100% arrest of all motion universe wide. This would include arrest of motion for everything, completely frozen, nothing moving anywhere. Under that scenario, as unlikely as it is, there would be "zero time".
It is my understanding of time that we do measure it, as you saw, on periodic motion. I'm not sure how time could ever be measured in any other way. Everything is always in motion whether you notice it or not, and it is all relative to the observer.
On that note, here is a fun thought experiment I had a couple of weeks ago:
Say a miner gets trapped in a mine shaft. He has absolutely no source of natural light down there (but he does have a flashlight the operates without batteries), and absolutely no communication at all to the outside world. He also isn't wearing a watch.
The miner, assuming he can somehow keep himself alive down there, decides that he'll keep track of the amount of time he's been down there based off of his usual sleep cycle. He knows that he's usually tired and asleep by 9, and awake and ready for the day by 5. So, he waits it out til he falls asleep, and then when he wakes up again he makes a mark on the wall. He's been down there for what he perceives to have been one night.
He does this over and over again, ticking off each new day as he wakes up. However the problem is, there is no way for him to know for sure if his system is accurate or not relative to time on the surface. He may think it is, but with no reference of time on the surface, his "days" could be off by a few days, a few weeks, a few years.... there is just no way for him to know for certain. Therefore, his only reference of time is sleeping and then waking again. For all he knows, he could have dozed off for ten minutes and awoke thinking it was all night. (I mean really, do YOU know how much time has passed for you between sleeping and waking without referencing something that will tell you).