What mystery? (spoilers)
Although the film is slow enough that my U.S. sensibility couldn't help spending the first part wondering "what's going on?", I wouldn't characterise the film as a "detective story" or a "mystery".
(I took the many times we hear but don't actually see a character to be more a clever way of dealing with a scarcity of acting talent than anything else.)
On the first viewing, with only a tiny bit of puzzlement, these interpretations came through to me: The other voices we hear -first in the car, later in the other rented room- are Behzad's two crewmen. Behzad and his crew have come to film the strange local ceremony that will take place when the old woman dies. They're using "treasure hunting" or "archaeology" (or perhaps "pot hunting") as a cover story to avoid offending the locals. The woman on the other end of the phone is Bezhad's handler for this particular assignment. The tension in the phone calls eventually builds so much that the woman suggests Bezhad should forego charging for the first two weeks, and Bezhad in turn asks straight out if there's actually a buyer lined up for the proposed footage or if it's just "on spec" ("serve as our pillow"). Near the end when a villager saw the crewmen in the morning not carrying any equipment, then didn't see them at all in the afternoon, it's a signal they've made their own decision and have "left" (even though it means hitchhiking). At the very end Behzad discovers that the old woman has died after all, but he can't run the movie equipment himself, and has to be satisfied with a few stills taken on his personal camera. The stills are of the villagers going to the ceremony rather than of the ceremony itself, and Bezhad has been sufficiently changed by his time in the village that he doesn't care any more.
Am I way off base? Is there really a mystery here that I'm missing?