What turns on the green blinking lights on the back of the watch and how do you turn them off?

Thank you for following up on the response.

The green LEDs are used by the heart rate sensor. It is normal for the sensor to take background measurements of your heart rate regularly throughout the day, but the LEDs do not remain permanently lit for this purpose.

You can disable the light by going to your Apple watch settings > select privacy > toggle the Heart Rate off.