The auto headlight light switch not working properly

This auto headlight system has a separate relay that is controlled by the BCM. So, when you turn the switch to auto, the BCM sees that and grounds this relay and then that is what turns the lights on through the switch.

So that means there is a chance this is a relay, BCM, or switch issue.

Let's start with checking the relay using this guide and then check for voltage coming out of it that goes down to the switch.

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

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

Please see the wiring diagram below and let us know what questions you have with this.