Welcome to 2CarPros.
The first thing I need you to do is remove the wiper relay and see if they still stay running. If they do, then we have a short to power between the switch and motor (brown/white) wire at motor. If the relay stops the problem, check the relay. Picture 1 shows the relay I am referring to and picture 2 shows its location. I highlighted each. Here is a link that explains how to check a relay:
https://www.2carpros.com/articles/how-to-check-an-electrical-relay-and-wiring-control-circuit
I Let me know what you find.
Joe
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Thursday, June 27th, 2019 AT 8:11 PM