Windshield wiper will continue to run after being turned off?

Hello,

It sounds like you might have a faulty switch.
There are probably worn connectors inside and when you try the mist is stays connected even when you release the switch.
When try to engage the washer fluid, can you hear the pump come on? If you do not hear the pump then you will have either a faulty pump or the switch could be bad.

Replacing the wiper switch does require removing the steering wheel.

Here is a helpful video:

https://youtu.be/Bkt9tfgJFdI

Check to see if you are getting power to the washer pump. If there is power but not operational then it can be either the pump of the switch.

https://www.2carpros.com/articles/how-to-check-wiring

I have attached diagrams for your reference.

Please let me know of any questions.

Thank you.