clockwise in peru

In the northern hemisphere a shadow rotates clockwise because the sun moves clockwise through the sky. The hands of analog clocks also move left to right as they’re built to imitate a sundial.

Do sundials move clockwise in the southern hemisphere?

No, they would move anticlockwise if you are south of the equator.

…which I have just remembered is called counterclockwise by Americans and other aliens.

Actually, sundials don’t move in either hemisphere.

Neither do shadows because they don’t exist.

well, sundials don’t move anywhere, at least the ones I’ve seen. But the shadow does move in different directions. It is easy to visualise.
The sun always moves from East to West so a shadow always moves from West to East. Now, if you are North of the sun, as you face north the shadow moves right (clockwise) but if you are south of the sun facing south, the shadow moves left (counterclockwise).

Note that outside of the tropics the sun is north or south of the observer all year round but in the tropics it can be north or south depending on the date.