could be a number of things, the motor, wiring, switch (it should turn on the motor by either spinning the end of the knob, or by pushing it away from the wheel)

can you move the wiper when its not on? (it could be a seized motor)

best thing to try is a new motor tbh, or connect a 9v battery to the terminals of the motor and see if it works then

Yeh basicaly what cinqy said! But I had this problem with my Punt when I first got it. Theres was a ticking noise coming from the back, and every time it ticked every light flickered! So I took it to a garage (silly me!) and they told me it was the earths and that they had fixed it. But no they hadnt So got a motor from the scrappy, fitted it myself (very easy) and bingo bango, no flickering and the rear wipper now works