You're correct that clocks measure time based on the oscillations of their mechanisms, whether it's a pendulum, an atom, or any other oscillating system. Time dilation can occur due to two different effects: gravitational time dilation and kinetic time dilation.
Gravitational time dilation, as I mentioned earlier, is caused by the influence of gravity on the flow of time. According to general relativity, the presence of a gravitational field slows down time relative to an observer in a weaker gravitational field. This means that clocks located in a stronger gravitational field will appear to run slower relative to clocks in a weaker gravitational field.
On the other hand, kinetic time dilation, also known as time dilation due to relative motion, is a consequence of special relativity. According to special relativity, when objects move relative to each other at high speeds, time appears to pass slower for the moving object relative to a stationary observer. This effect becomes significant as objects approach speeds close to the speed of light.
To understand what acts on the mechanism of a clock to cause kinetic time dilation, we need to delve into the principles of special relativity. Special relativity states that time dilation occurs because the fundamental nature of spacetime changes when objects are in relative motion. When an object moves at high speeds, its motion affects the geometry of spacetime, causing time to pass differently for the moving object.
In other words, the mechanism of a clock is not directly acted upon by any external force to cause kinetic time dilation. Instead, the movement of the clock itself, relative to another frame of reference, alters the way time is experienced within that moving frame.
To summarize, gravitational time dilation is caused by the influence of gravity on the flow of time, whereas kinetic time dilation arises from the relative motion between observers. Both effects have been experimentally confirmed and are integral parts of Einstein's theories of relativity.