Windshield wipers issue

I am not sure I understand what the wipers are doing. When you say they are wacky, does that mean they operate on their own or that they are not wiping in tandem?

Can you get a video of what this is doing?

Also, the washer fluid that is working when the engine is off. Does that mean they are spraying at all times?

If that is the case then you most likely have a stuck relay. I included the wiring diagram below. We are going to have to check voltage coming from the relay to confirm this.

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

https://www.2carpros.com/articles/how-to-check-an-electrical-relay-and-wiring-control-circuit

Let us know what you find with this.

When I say wacky; first they started running without them being turned on, and turning them on would work too but not at the intended speeds. I changed the wiper motor with one I got on rock auto and all seemed fine for a minute but the wipers wouldn't go back to their parked position when turned off. Then I changed the wiper switch on the column. That worked for a moment then the wipers quit working but the washer fluid started squirting, but not fully, on their own and the wipers wouldn't work. Not good while driving. When I actuate the washer fluid, it would squirt properly. When not actuated they squirted with low pressure. I parked the car and came back with a dead battery (New). So I disconnected the battery and am thinking of changing the wiper motor again... I checked the big SMJ plug on the passenger side kick panel and it looked new, but did not access the relay and fuses at that location.

By the way your help is greatly appreciated.
I have read that the usual culprit is the wiper motor.

You are correct. The wiper motors are kind of an all encompassing part. So if they are getting power then they take care of it them selves.

However, I would check and clean both grounds. The washer pump and motor share a ground so if that is loose or dirty then you are going to get all sorts of crazy function.

G204 is on the left kick panel.

G201 is behind the dash on the passenger side.

They don't have a diagram showing this location but they should be pretty obvious in that area.