Is there such a thing called a starter sensor on the automatic V-6?

Good evening,

No, there is not. The system has a relay and wiring to the starter.

I would start by cleaning the battery cables really good of all corrosion inside and outside.

https://www.2carpros.com/articles/everything-goes-dead-when-engine-is-cranked

Then when it will not start, check the purple wire at the starter solenoid for power in the start position to see if there is power coming.

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

https://www.2carpros.com/articles/how-to-use-a-voltmeter

Roy