Why does the second hand of a clock sometimes seem to pause when you look at it?

Because your brain hides the gap. Eyes move in fast jerks called saccades, and vision is suppressed during them - you would otherwise see a smear several times a second. To cover the missing time, the brain backfills it with whatever it sees when the eye lands, and stamps that image as having started earlier than it did.

So the first second you see appears to last longer than a second. The effect is called chronostasis, and it works with sound and touch as well as vision. It is also why you can never catch your own eyes moving in a mirror: look from one eye to the other and you see two still images, with the movement between them edited out.

The amount of time you are functionally blind adds up to something like 40 minutes of a waking day. None of it is noticed, because the brain is not showing you a video feed - it is showing you a constructed account, stitched together and presented as continuous. The stopped-clock illusion is one of the few places where the join is visible.