You're correct that Galileo didn't have access to accurate clocks to measure the pendulum's motion directly. However, he devised a clever experimental method to investigate the pendulum's behavior and discover its isochronism, which means that it swings at the same frequency regardless of its amplitude.
Galileo made his observations in the late 16th century, long before the invention of accurate pendulum clocks. To study the pendulum's motion, he used his own pulse as a rough timekeeper. He realized that the beats of his pulse could serve as an approximate measure of time.
Galileo performed his experiments by using a simple setup involving a swinging lamp or chandelier. He would observe the motion of the swinging lamp and compare it to the rhythm of his pulse. Galileo noticed that the lamp seemed to swing back and forth at a steady pace, and he found that the time it took for the lamp to complete a swing (from one extreme to the other and back) was consistent, regardless of the amplitude of the swing.
By carefully observing the lamp's motion and matching it with the timing of his pulse, Galileo concluded that the period of a pendulum (the time taken for one complete swing) remained constant. This discovery was a significant breakthrough because it meant that the pendulum's motion could potentially be used as a reliable timekeeping mechanism.
Although Galileo's experiments provided initial insights, it was later scientists, such as Christiaan Huygens in the 17th century, who further refined the understanding of pendulum behavior and developed accurate pendulum clocks based on this principle. Nonetheless, Galileo's work laid the foundation for the understanding of the pendulum's regular motion and its significance in timekeeping.