I have a weird problem (well, not me personally, you understand...)

Every time I start the car, the rear wiper starts, goes for half a dozen wipes, then stops. (but parks anywhere). It doesn't matter if the wiper has been switched on or not.
When I do switch the rear wiper on to auto-wipe, it will, again, only do half a dozen wipes, then park and not work again unless I toggle the switch.
Any ideas please? It's driving me nuts (and probably not doing the rear window any good by 'scraping' dry)
Thanks for any help