I have a 68 Camaro. The wipers only work when you push in the washer knob. This works with both high and low speeds. My 71 Corvette does exactly the same thing. I have replaced the switch on both vehicles and that didn't cure it. Anyone seen this before ?

If I remember correctly one of the wiper motor grommets has a ground strap that grounds through one of the mounting bolts. Check to make sure they're clean and tight.