To determine the timing mechanism of a grandfather clock, it is essential to understand whether it completes one full oscillation or half oscillation in one second. The discussion clarifies that the oscillation rate varies by clock size, with large grandfather clocks typically completing one full oscillation (1 theta) per second. In contrast, smaller cuckoo clocks may complete four (4 theta) or two (2 theta) oscillations per second. The ticking sound of the clock can help identify its oscillation rate, and users are encouraged to seek video demonstrations for further clarity. Understanding these mechanics is crucial for accurate clock operation and maintenance.