I know what you are talking about and this is the PASS III System, I know how to do the procedure because I've done it before. I just don't know exactly what resistor I need, on the key switch it may be written on it somewhere so I have to get it apart and see. I'm hoping to get the resistor in and the light turns off since it's on because there's a problem in the circuit. Keyless Entry works fine so I don't think its the BCM.Can you do a relearn? Or is that too new? When I did a power train swap on another truck it turns out the VATS module on the truck was not getting along with the PCM. I bypassed the whole column resistor and added one that was within the range of the system, and did a relearn which consisted of starting the truck and letting it die. Let it sit with the key on 10 minutes, fire it again let it die and sit, and on the 3rd or 4th round it learned the new value and stayed running. Saved me $120 on credits so I didn't have to tune it out and sold that pig for moneys.
Given I put a Cam in and tuned the truck for that, PCM is unlocked to my stuff so fortunately it was just hook up and turn the VATS off and I'm able to drive it. The light will be a more involved process.