Is the question, how was it possible to measure a second precisely? I can provide a partial answer. Mechanical clocks appear in the 13th c. They had a simple movement- a falling weight powered an escapement mechanism that somewhat resembles modern mechanical clocks, with a verge: an oscillating fork pivoting back and forth to allow a toothed wheel to advance, tooth by tooth. But there was no pendulum: the verge was mostly controlled by friction, and no doubt someone had to re-set the clock by sundial regularly. This was probably good enough precision for the time. Some German clocks had second hands by the 16th c., when spring-driven mechanisms began to be used: but for the most part, few clocks needed them. Few people needed it: because, really, who then would NEED to know time down to the second? A medieval clock could be handy for telling monks when to celebrate lauds, matins, etc. but an hour hand was good enough for that. And was good enough for most purposes- when to meet someone, when to go to dinner.

In 1581 Galileo noticed how regular pendulums were, in their swing ( supposedly watching a hanging lamp in the cathedral in Pisa, realizing that, no matter how far it swung, the time for each swing was the same), but only asked his son to build clock based on the idea in 1641- which he didn't finish. Here's one reconstruction: it doesn't have a second hand, either. But the insight of how a pendulum worked was very useful for both clock design and a group of people who did find it very handy to know time, down to the second: musicians. Musicians began using pendulums sometime in the 17th c., to carefully keep track of tempo. Thomas Mace, in his 1676 Musick's Monument, advised the student to hang up a pendulum, and it was only a little later that graduated pendulums began to be used, the first by Etienne Loulié in 1696: here's a French site with illustrations of it. By the 1780's, clockwork+ pendulum tempo-measuring mechanisms were being developed, which soon became the familiar wind-up metronomes. By then, of course, there was general demand for precise time, and even pocket watches would tell seconds.

An excellent book- a classic- on how an increasing demand for measuring smaller increments of time pushed clock design is David S Landes: Revolution in Time