(I only now read the op)Jesus' will to live was the will of the flesh. Like in any of us there was an instinctive [proper usage?] desire or purpose to keep himself alive [physical life] and comfortable. Jesus showed us by example what God hopes for from each of us... to make our way equal to God's Way.
Some people say Jesus could not have denied God's Way, but I have to disagree, because Jesus had to have a real temptation with the real possibility of giving the wrong answer... or to me anyway... it loses the meaning of temptation.
If Jesus had succumbed to any temptation, we would all be talking in vain emptiness, without any hope, and being most foolish of all men anywhere.
He laid down His life freely, perfectly in obedience and total harmony with the Father , all of His Word, all of His Plan, and all of His Purpose Eternally.
The temptation as if to stand up for Himself, in any way to protect His Own Life not trusting His Father to ,
if given in to,
would have meant He could not have been or become our Savior - His blood could not be the Atonement, the Payment once for all time, for out sin(s).
Oh, yes, He "could" have sinned, but then that would not have been His Plan nor the Father's Plan, would it ? Something totally different would have resulted.