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Ohhhhhhhhhhhhh Yeaaaaaaaaaaaaaaaaaa! There is a common C5 issue that can cause this problem. There are three windshield cowl drains on the drivers side. They look like this:
If the drains clog up, they can cause your wipers to have issues. Sometimes they will come on all by them selves and sometimes they will not work at all.
You can access the drains by sticking your hand in this area:
If the drains are HARD they will be packed with trash and GOOK like this:
Please let me know if this fixes your problem and if you have any more questions.
I agree with Bill. Almost sure your problem is clogged drains. When clogged, water will submerge the control module mounted under the wiper motor and short out the system. Replacement module from Dealer = $100.00....everyone should make sure this drain is clear