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Had the same thing happen to me.... find the udders under the wiper motor on the driver's side...pull them off and clean them out, they are likely filled with gunk. Pull the fuse and let the motor dry out for a few days or more, replace the fuse and you should be good to go.
My 02 z06 came on one morning and would not go off. Pulled the fuse and took to dealership. They replaced the wiper switch about $250 and $250 for labor!
Hard rain, even with clean udders...flooded the damn motor again....tonight --- took it out, dumped excess water, sprayed electrical contact cleaner all over circuit board, removed stupid udders and cut all ends off, replaced everything all is fine.
Just shows even with clean udders a hard rain can fill up motor area fast. The tight udders slits can't handle the flow and backs up.