I wish I could give you a answer. I worked with these system a lot at GM. What I can confirm is you are not the only one to have a illuminated security light and nothing happening with the car.
You could be on the other side of the coin with these systems, a car that won’t crank with no apparent activation of the security stytem.
The Factory Service Manual gives a good overview of the system complete with Body Control Module re-programing steps but it hasn’t helped me solve the two conditions I have described.
You are not alone with this mystery light. Like I said it can get worse,with the car not cranking,we have many posts on this Forum with this problem with Passlock 2 systems. My only answer is that I still don’t understand the sysyem sufficiently.