Citroen Xsara Picasso rear wiper problem

Rear wiper activates when vehicle is unlocked either with the remote or manualy with the key. The wiper then runs for aprox. 30sec. and randomly parks. The rear wiper also activates when ever reverse is engaged, I know that the rear wiper is designed to automaticly opperate when the windscreen wipers are switched on and reverse engaged but this is happening every time I engage reverse. I have been loathed to have this fault diagnosed, as I feared the costly replacement of some sophisticated electronic componant. If any body out there has any ideas or solutions to this problem I would be most gratefull.