How do I fix my rear wiper - works sporadically?

The rear wiper on my car does not work when using the stick inside on the steering wheel. The water comes from the compartment and runs down the window, but the wiper fails to engage to clear it. When I lock the car using my key in the drivers door to lock, all doors lock except the boot, and the wiper moves halfway across the back window. If i second turn the key and deadlock the car, the wiper moves another halfway and clears the full window. Any suggestions? Could this be a relay? It is not the fuses as I have checked all of them and they are intact.