Indexing? I thought that meant removing the wiper arms and putting them in a different position manually? Do our cars do the indexing automatically somehow? If there is something that controls that and it's gone bad, that would make sense. The wipers actually "park" in different locations, sometimes further up the windshield than others.

Yes, the wipers work as normal in position 2 and 3 (constant speeds).

Wiper module hasn't been replaced in the year that I've owned the X...I think that the wiper module on an E53 is actually the General Module (GM III). That is indeed behind the glovebox. From my research, it is prone to various failures, but mostly windows and locks.

Now that I think about it, about the time this started happening, my X was at an indie shop to troubleshoot window problems. The GM also controls the driver windows. They used an AutoLogic to check the programming somehow; maybe that inadvertently broke the rain sensor. I will probably end up taking it back there to have them look at this, since they're able to troubleshoot a lot better.