Here’s a design for a passive polarization clock.
The sky is polarized in concentric circles around the sun. The polarization of the southern sky moves through around 180 degrees during daylight hours. It is polarized vertically in the morning, horizontally at noon, and vertically again in the evening.
Align slices of polarized film such that they are parallel to the contours. Any given ray from the center of the sundial outward always hits the contours at the same angle; the angle changes by 360 degrees as the ray passes through 180 degrees. In other words, the clock goes from 6am to 6pm as the sun moves through the sky.