security light on code p1626 after installing rebuilt starter

[04snake]

The car starts but the security light has come on solid, not flashing and has stayed on since installing a rebuilt non OEM starter. Could the relay or relay ground be causing issues with BCM? Never saw the light after turning the car over before replacing the starter. I have a p1626 code as well but I see where that is not that unusual and I don't know that will cause the light to be on. If the ignition tumbler needs to replaced OK but I see where some guys ground the starter relay differently to kill this light to bypass the BCM.

should I have the someone scan for BCM codes, if so what am I looking for?

I just don't want to get stranded somewhere when it decides to go into full VATS override.

[04snake]

I cleared the p1626 code, didn't come back, car still starts OK but the security light is still on. Man I hate staring at lights that I can't fix.