Yakov would not be ‘in a deep sleep’ because how didn’t the embalmers notice his breathing ?
And his pulse ?
It says they thought him being dead ?
It could be that his brain was functioning bederech nes without oxygen supply, and that was the measure of life within his body.
Thats why it does not say vayamat.
This is indeed a plausible explanation, I don’t know. I was just bringing how the meforshim explain the word ויגוע here.