You should definitely look to the silent work of Buster Keaton. Keaton
was reared in vaudeville and shows a lot of that heritage in his short
_The Playhouse_. There are theatre references in much of his work.
As for books on Keaton that would include the information
that you are looking for, look for _Buster Keaton and the Dynamics of
Visual Wit_ which is George Wead's dissertation. Also _Keaton: the
Silent Features Close Up_ by Daniel Moews.