These are gathered scriptures regarding the 8th Day Assembly
Leviticus 23:33 ¶ And the LORD spake unto Moses, saying,
Speak unto the children of Israel, saying, The fifteenth day of this seventh month shall be the feast of tabernacles for seven days unto the LORD. On the first day shall be an holy convocation: ye shall do no servile work therein. Seven days ye shall offer an offering made by fire unto the LORD: on the eighth day shall be an holy convocation unto you; and ye shall offer an offering made by fire unto the LORD: it is a solemn assembly; and ye shall do no servile work therein. These are the feasts of the LORD, which ye shall proclaim to be holy convocations, to offer an offering made by fire unto the LORD, a burnt offering, and a meat offering, a sacrifice, and drink offerings, every thing upon his day:
Beside the sabbaths of the LORD, and beside your gifts, and beside all your vows, and beside all your freewill offerings, which ye give unto the LORD. Also in the fifteenth day of the seventh month, when ye have gathered in the fruit of the land, ye shall keep a feast unto the LORD seven days: on the first day shall be a sabbath, and on the eighth day shall be a sabbath.
And ye shall take you on the first day the boughs of goodly trees, branches of palm trees, and the boughs of thick trees, and willows of the brook; and ye shall rejoice before the LORD your God seven days. And ye shall keep it a feast unto the LORD seven days in the year. It shall be a statute for ever in your generations: ye shall celebrate it in the seventh month. Ye shall dwell in booths seven days; all that are Israelites born shall dwell in booths: That your generations may know that I made the children of Israel to dwell in booths, when I brought them out of the land of Egypt: I am the LORD your God. And Moses declared unto the children of Israel the feasts of the LORD.
8066 shemiyniy, shem-ee-nee’; from 8083; eight:-eight.
8083 shemoneh, shem-o-neh’; or shemowneh, shem-o-neh’; fem. shemonah, shem-o-naw’; or shemownah, shem-o-naw’; appar. from 8082 through the idea of plumpness; a cardinal number, eight (as if a surplus above the “perfect” seven); also (as ordinal) eighth:-eight ([-een, -eenth]), eighth.
6116 `atsarah, ats-aw-raw’; or `atsereth, ats-eh’-reth; from 6113; an assembly, espc. on a festival or holiday:-(solemn) assembly (meeting).
In the Talmud, Shemini Atzeret is called Atzeret shel Chag / “Eighth Assembly”
1st Kings Chapter Eight ~ Whole chapter = One nation united in Jerusalem
1st Kings 8:66 On the eighth day he sent the people away: and they blessed the king, and went unto their tents joyful and glad of heart for all the goodness that the LORD had done for David his servant, and for Israel his people.
Pay close attention to the last scripture, read slowly
2nd Chronicals 7:7-10 Moreover Solomon hallowed the middle of the court that was before the house of the LORD: for there he offered burnt offerings, and the fat of the peace offerings, because the brasen altar which Solomon had made was not able to receive the burnt offerings, and the meat offerings, and the fat. Also at the same time Solomon kept the feast seven days, and all Israel with him, a very great congregation, from the entering in of Hamath unto the river of Egypt. And in the eighth day they made a solemn assembly: for they kept the dedication of the altar seven days, and the feast seven days. And on the three and twentieth day of the seventh month he sent the people away into their tents, glad and merry in heart for the goodness that the LORD had shewed unto David, and to Solomon, and to Israel his people.
There are eight days of celebration in Hanukkah.
1st Kings 8:1-2 ¶ Then Solomon assembled the elders of Israel, and all the heads of the tribes, the chief of the fathers of the children of Israel, unto king Solomon in Jerusalem, that they might bring up the ark of the covenant of the LORD out of the city of David, which is Zion. And all the men of Israel assembled themselves unto king Solomon at the feast in the month Ethanim, which is the seventh month.
Solomon gathered the people together not just to dedicate the temple but to re-dedicate themselves. This temple was built in Jerusalem.
The Shemini Atzeret morning service includes the Yizkor service, as well as a special prayer for rain, officially launching the Mediterranean rainy season. (Prayer for the latter day rains.)
This is analogous to a king who invited his sons to a feast for a number of days. When the time came for them to leave, he said: “My sons! Please, stay one more day; it is difficult for me to part with you!” (Midrash)
The people sing The Song of the Watchman
Isaiah 52:7-12 ¶ How beautiful upon the mountains are the feet of him that bringeth good tidings, that publisheth peace; that bringeth good tidings of good, that publisheth salvation; that saith unto Zion, Thy God reigneth! Thy watchmen shall lift up the voice; with the voice together shall they sing: for they shall see eye to eye, when the LORD shall bring again Zion. Break forth into joy, sing together, ye waste places of Jerusalem: for the LORD hath comforted his people, he hath redeemed Jerusalem. The LORD hath made bare his holy arm in the eyes of all the nations; and all the ends of the earth shall see the salvation of our God. Depart ye, depart ye, go ye out from thence, touch no unclean thing; go ye out of the midst of her; be ye clean, that bear the vessels of the LORD. For ye shall not go out with haste, nor go by flight: for the LORD will go before you; and the God of Israel will be your rereward.