If I said the sun "sits in the West" it would mean something completely different

Exactly. It's not used that way. However, one normally sets something down transitively; if something sits, it's doing it on its own. When I sit in a chair I do so intransitively. I can set the book on the table, but I do it transitively. That the sun sets intransitively is an exception. It could be argued that the sun isn't setting, the horizon is coming up but I think that realization post-dates the normal usage by a few years.