House of Sand and Fog (2003)
Kathy's shadow in doorway/Ethan's shadow in doorway--explicitly noted in the commentary as a Searchers riff.
Mentioned by name
When Rachel is browsing through the videos at the fair, House of Sand and Fog is one of them
Krusty mentions that he and Sideshow Bob have watched this movie.
A clip is shown in "Conan on the Aisle".
A clip is shown
Clip included in montage of Ben Kingsley films