The clicking is the solenoid pulling in. You cannot assume that means that the contacts on the high current side are working, so
Have you got, can you borrow a multimeter ?
You need to check that there is 12v to the high current side of the relay. Then do a continuity check between the high current ouput of the relay connector to the terminal at the wiper motor.
Daft check - I did read a post somewhere wheere someone had this type of problem and they later found out the rear wiper would not operate if the tailgate was open.