Is there any kind of funky thing they could do to have it rotate slow enough to take an entire night to cross the sky? something like a lagrange point perhaps (stationary relative to sun?)
The Lagrange points are weird because they orbit two things at the same time. There should be more normal orbits somewhat lower than geostationary that cross slowly, but they would also be out of sight for a long time.
Then I suppose the idea would be to find an orbit where that long time is equal to one day - obviously, the length of one day on a given section of the planet keeps changing, so perhaps you only turn on the light after a certain amount of time or find some orbit that mimics whatever the sun is doing if thats at all possible