What observational technique is suggested for visibly demonstrating Polaris's relative lack of movement compared to background stars?
Using a camera capable of long exposures (3 to 4 hours) pointed at Polaris.
A practical, yet time-consuming, method exists to visually confirm the differential motion between Polaris and other stars, relying on photographic evidence. This involves setting up a camera capable of collecting light over an extended period, specifically suggested to be between three to four hours, with the lens aimed directly at Polaris. During this long exposure, stars farther from the pole will register their apparent rotation as curved trails or arcs. In contrast, due to its near-perfect alignment with the north celestial pole, the light from Polaris will register as only a very short, tight arc or perhaps appear as a slightly thickened point, offering clear visual proof of its relative stability against the backdrop of the trailing stellar field.

#Videos
Why is the North Star Always in the Same Place? - YouTube
Why Do Stars Draw Circles Around Polaris? - YouTube