I was reading a book called "The Life and Times of Jesus the Messiah" by Alfred Edersheim, and the author refers to different rabbinical writings and historical writings.
What I found interesting was the timing of Jesus, because He waits till the part of the feast where a priest has poured out a vessel of water that has been taken from the pool of Siloam (means "sent"). The people recite some psalms called the great "Hallel" (Psalm 113 to Psalm 118) and call upon God to work salvation.
He waits till the ceremony is done and then proclaims it's fufillment as being in relationship to Himself. In the ceremony a drink offering of wine was first poured out. Let us not forget that the pouring out of Jesus blood was first and always should be first to the receiving the blessing of the gift of the Holy Spirit.