We've all heard the phrase ugly enough to stop a clock, but what happens when that is actually the case? For starters I challenge you to find an analog clock, and preferably not be the creepy old guy at the elementary school. Found one good...
When you first stare at the clock, you may notice that the second hand appears to freeze briefly before taking on its regular cadence. This highlights the perception versus the reality of time itself.
When the eyes move, they experience a brief interruption of persistence due to rapid eye jumps called a saccade. The brain basically has momentary blindness as it ignores stimuli to start processing the new data. At the same time, so we don't appear to be walking around in a world of strobe lights, it attempts to backfill in the missing data. You are unlikely to realize that over the course of a day your brain spends nearly 40 minutes filling in blind gaps.
Some more fun tests, look at a mirror and quickly move your focus. Anyone else looking would see your eyes dart around, but you are unable to do so.
There is also theories floating around for audio chronostasis. Where the time between phone rings and durations appear different. Or even yawning making music slow down.
So perhaps Ponce de Leon didn't actually find the Fountain of Youth, but rather just moved his eyes around fast enough to slow down time. He probably should have made a flux capacitor instead.