This picture of Hollywood/Cherokee must've been taken around the same time as those posted by
Martin Pal. USC dates it at circa 1936/1958. The same picture can be found at hollywoodphotographs.com where it's dated 1937.
USC Digital Library
Here's a close-up of the box on the roof. It appears to have a ladder and hatch at the rear, but otherwise I'm none the wiser. The sign on the corner of the building states that the "owner will erect new building".
Detail of picture above.