The rear wiper on my 09 A4 Avant has a mind or its own. Initially it simply started parking randomly. Then it began continuous running instead of intermittent and would eventually stop completely. Park was still random. Off and on would restart it. Yesterday it would start by itself and run continuously in dry conditions even though the stalk was in (both) off. Nothing seemed to stop it. Eventually it would stop, but only after 20 minutes or more of unnecessary running. Then it would start again. It seemed like indicating right to change lanes could trigger it. I was on a long drive at the time so didn't want to stop. Any ideas? 

You could get a diagnostic check to see if any fault codes flag up. I suspect it's a faulty stalk. 

Hello Ian,

Worth checking the wires in the flexible harness section that runs from the body to the tailgate. Wires can become brittle in colder weather and fracture and possibly contact other partly fractured wires. Always worth an initial elimination of this being the cause. 
Perhaps you could let us know how you get on. 

Kind regards,

Gareth. 

hi ian,id say you need to replace the motor and check for leaks before fitting the new one.water has gotten into it and theyre the symptons your getting