I am wondering exactly how to troubleshoot the started circuit on this vehicle.

It's difficult to do as it seems all electrical goes thur the Body Control Module. This can cause the headlights to turn on when you close the front door or no response to turning the key to start( even with known good battery ). May have contributed to abs light on as well(with no fault codes). (Events are personal experience) The bcm is a nightmare as replacement requires reprograming by the dealer($$!). Not the best GM produced device, dont know why it's required. Although it will shut off your lights after 10 min if they are left on. Located where a glove box should have been, below pass. air bag.