I agree with
@TJBaker57 completely.... FWIW... I think I have an idea on how this problem developed:
(1) The Steady Headlight Drain on the Battery can weaken it and ruin the Battery Cells if Drained and Re-Charged many times before this problem could be discovered.
(2) Even after the Engine Starts and the Battery ostensibly takes on a new charge... The system runs off of BATTERY POWER.. .NOT ALTERNATOR POWER. So if the Battery has suffered enough internal damage, the cascade of this problem would follow in (3)...
(3) The PCM is VERY Sensitive to Insufficient Voltage and according the "Pinnacle of GM OBD2 Scanners"... The OEM GM Tech 2 Scanner uses an OEM DC to DC Voltage Conversion mechanism is to ensure that the Tech 2 can operate within a Min-Max range of 8 Volts DC to 20 Volts DC. However ALL of the After Market Voltage Regulator "Chips" in the "GYMKO" flavor Tech 2s only function between 9 Volts DC to 18 Volts DC.
(4) The GM, Single Wire Class 2 Network operates within a range of 0 Volts DC to 7 Volts DC oscillating generally in the 0-5 volts DC Range.
(5) If the HIB Module(s) were being fed Volt DC via a problematic Voltage Relay in the Power Distribution Center...AND there was a Short to Positive in the Electro-Viscous Fan Clutch... Even with the Engine running and the Alternator throwing 13.5 + Volts DC into Bad Battery... Once the Vehicle is Shifted into Drive ... the Engine and Transmission System load vs. Voltage demand might DROP below the 8-9 Volts DC Lower Threshold powering the Class 2 Network.. and this would involve the Power Feed to the OBD2 Dash Panel Female Connector in particular.
(6) The conclusion might be that the Problem with the OBD2 Scanner is NOT a Cause... but rather is a Symptom of these Recombinant DC Electrical issues. There is probably nothing wrong either with the Port itself ... or with the Wiring in between all of these Class 2 items in communication with one another...and the PCM-BCM.