In Jack Thayer's "Survivor's Account" he says;
"The ship was in front of me, 40 yards away. How long I had been swimming under water, I don’t know. Perhaps a minute or less. Incidentally, my watch stopped at 2:22 am."
He seemed to believe he had not been swimming away from the ship for long after he jumped into the water. If his watch stopped at 2:22am when he entered the water that does not coincide well with a jump much earlier than this time.
In the next line Jack says;
"The ship seemed to be surrounded with a glare and stood out of the night as though she were on fire."
I take this to mean the lights were still on after he had entered the water.
In this last line of interest he says:
"She continued to make the same forward progress as when I left her. The water was over the base of the first funnel."
I hope this information will help.