Had same problem a couple of months ago. In my case it turned out not to be the switch and it wasn't the motor either. It turned out that the passenger side blade pivot was corroded internally and almost could not be turned. The wiper motor did not have enough power on low speed (which includes wash) but could move it on high speed.
I disassembled it (beat it apart) clean the corrosion out, lubed it and reassembled it and found that my high speed had actually been closer to low speed and WOW, do I have a high speed now.
Before you pull apart the wheel, stalk and wiring take the 15 minutes to disconnect the wiper linkage from the motor and see if the motor behaves properly. At least you will know if it is electrical or mechanical.