I thought that the problem may be with the multi- function switch that turns the wipers on, but after replacing it with a new one, the wipers still do not work. The problem with your windshield wipers is probably due to a faulty windshield wiper motor. In all probability if you replace it, your problem will be solved. I have looked at the switch, it is in perfect working order, and I can hear rapid clicking coming from behind the dash when the wipers are not working correctly. When wipers are on intermittent, they will stop in various places on the windshield.
Wipers work fine in slow or fast mode.
Motor sounds like it should sound. From what you have described, we believe your windshield wiper switch may be defective. I have problems every now and then, mostly when it rains , I wash the car, or when the weather is heavy, my windshield wiper fluid and wipers on the front lights just go haywire. My original windshield wipers come on and my park lights come on, not all at one time but usually one or the other. I have taken the fuses out of the wiper fluid and the windshield wipers and kept them out to stop it from coming on but the park lights still come on when something underneath the hood gets wet and stays on long enough to drain the battery.