Apologies for any confusion caused. You are correct, time dilation is observed when comparing clocks that are in relative motion or experiencing different gravitational fields. If two clocks are stationary relative to each other, they will not exhibit time dilation in relation to each other.
Time dilation becomes apparent when comparing the ticking rates of two clocks in different frames of reference. For example, if one clock is in motion relative to another, observers in each frame of reference will measure different rates of time passing for the other clock. Similarly, if one clock is in a strong gravitational field and another clock is in a weaker gravitational field, they will measure different rates of time passage relative to each other.
In practical terms, to observe time dilation, clocks need to be in different frames of reference or gravitational environments. By comparing the time measured by these clocks when brought back together, the time dilation effect can be measured. This has been done in various experiments, such as using highly accurate atomic clocks on airplanes or satellites and comparing their readings to clocks on the ground.
To directly observe time dilation with stationary clocks, it would require manipulating the gravitational field around one of the clocks or somehow accelerating one of them to significant speeds. However, in our everyday experience on Earth, the effects of time dilation due to motion or gravity are typically too small to be detected with stationary clocks.