The eighth day cannot be the last day of the feast in John 37:7 either, because God does not change something like that. Nehemiah has something to say about this that really makes it clear.
That is so clear. The Feast of Tabernacles is seven days long, and the eighth day is a separate festival. So when John wrote what Jesus declared on the last day of the Feast of Tabernacles, it was the seventh day of the feast. It was on the seventh day of the Feast of Tabernacles and not on the Last Great Day
Let us throw in a little bit of logic here. Even as Passover is a festival distinct from the Days of Unleavened Bread, how could Passover be the last day of the feast? It is a separate festival. It is a one-day festival. How can you call a one-day festival the last day of the feast? Pentecost is one day long. Can we call it the last day of the feast? There is no logic there. The same is true with Trumpets. The same is true with Atonement. It is only those festivals that have more than one day that there can be a first and a last day, and that is Unleavened Bread and the Feast of Tabernacles. So, the last day of the feast in John 7:37 is the last day of the Feast of Tabernacles.
The eighth-day festival is mentioned only five times in the Bible: Leviticus 23:36, and Leviticus 23:39. That is two of them right there. Numbers 29:35 is three. II Chronicles 7:9 is four, and Nehemiah 8:18 is five. That is the extent of the mention of what we call "the Last Great Day" in the Old Testament.
Now what is the eighth day called in the Old Testament? It is translated as either "sabbath rest," "holy convocation," or "sacred assembly." No other names are given to it. The Hebrew words that are translated into those terms is Shemini Atzeret. Shemini Atzeret means "sacred assembly." It means "holy convocation." Incidentally, that is a term that is used frequently in the Bible.