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Possible engine oil cooler ruptured.
Remove it and look for debris or see if it wobbles from wear. Possible replacement needed.
If I remember right, remove the screws holding the light in and drop it down to replace the bulb.
I have rebuilt many of GM rear ends. Either a tag or check with the dealer with your VIN # for more info on the gear ratio.
Have the battery and charging system tested, possible dirty battery connections.
O'Reilly has them reasonably priced, around $60.00.
Have the engine light scanned for codes, and post the codes.
It could be, but without seeing or hearing it, can't be sure.
It's supposed to, The computer removes all access engine loads to try and allow it to cool down. Find the cause of the overheating.