I thought it was the washer pump at first. I replaced it and it still has the problem. I hope it's not the switch, because the switch on the dash is impossible to find. Any idea on what could be causing this? Could it be the wiper motor since the two are tied together?

 

Solved it on mine,

the spring that pulled the the wheel of the pump was not how it suposed to be.

check by disconect the pump wires if it does it anyway it is or the gear set wrong (that moves with the wipermoter) or in front of the pump the springs that conect or disconect by a magnet is wrong.

Il had to disconect the pickup hose on the way home

 

Well the original wouldn't turn off and it eventually burned out. I replaced it with another one and it still does it. It's not the washer pump. I've read on another forum that it's probably the wiper motor that is not closing the circuit on the power to turn off the power. I hope this does the trick.

 

easy to check.

remove the washer pump and you'l see the pal that moves when you turn on the whipers.
it's having a park position wich when you turn on the whipers it moves out to and stay's out.

But when you stop the whipers it has to go to the park position.
It works with a tensionspring

 

I finally got it fixed. It was the wiper motor.