I haven't found the verse that says "the Holy Ghost is our rest"?
God threatened Judah saying He would speak to them via foreign conquest (stammering lips and another tongue) yet they would not listen. His message was was about rest, this is the rest, etc. Jeremiah however explained what that rest was:
Jeremiah 6:16 KJV
Thus saith the Lord , Stand ye in the ways, and see, and ask for the old paths, where is the good way, and walk therein, and ye shall find rest for your souls. But they said, We will not walk therein .
Rest for the soul is found in "the old paths wherein is the good way". Rest is cessation of certain activities. The number one rest that people need is a cessation from fighting God. That is why rest and peace are so closely connected. It is an absence of war or enmity between man and God.
Now don't get me wrong, there can be no genuine rest apart from or outside of the Holy Ghost. But why is that? It is not because of some catharsis or emotional release, but because the Spirit brings freedom from the bondage of sin (disobedience).
As for the Sabbath day itself, God told Israel why He commanded it:
Exodus 31:15-17 KJV
Six days may work be done; but in the seventh is the sabbath of rest, holy to the Lord : whosoever doeth any work in the sabbath day, he shall surely be put to death. [16] Wherefore the children of Israel shall keep the sabbath, to observe the sabbath throughout their generations, for a perpetual covenant. [17] It is a sign between me and the children of Israel for ever: for in six days the Lord made heaven and earth, and on the seventh day he rested, and was refreshed.
The reason given is "for in six days the Lord made the heaven and the earth, and on the seventh day He rested, and was refreshed." Sabbath keeping was a sign between them and God, it identified their God as the Creator of all things and thus the one and only true God. It was a banner if you will saying who their God was and to whom they belonged.
Some will say "Well then, it was a sign for those people, but not for me." However, the church IS ISRAEL. Not a new replacement Israel, but the same Israel of old, under a new covenant through Messiah. Moreover, this sign given to Israel is based on His work (and rest) as Creator of the universe, and since all mankind has one Creator, all should revere and honour Him. It was a sign limited to Israel by the fact only Israel worshipped the One God Creator and Father of all.
God expected the nations to learn from Israel and follow His ways:
Deuteronomy 4:5-8 KJV
Behold, I have taught you statutes and judgments, even as the Lord my God commanded me, that ye should do so in the land whither ye go to possess it. [6] Keep therefore and do them ; for this is your wisdom and your understanding in the sight of the nations, which shall hear all these statutes, and say, Surely this great nation is a wise and understanding people. [7] For what nation is there so great, who hath God so nigh unto them, as the Lord our God is in all things that we call upon him for ? [8] And what nation is there so great, that hath statutes and judgments so righteous as all this law, which I set before you this day?
He said it would come to pass:
Isaiah 2:2-5 KJV
And it shall come to pass in the last days, that the mountain of the Lord's house shall be established in the top of the mountains, and shall be exalted above the hills; and all nations shall flow unto it. [3] And many people shall go and say, Come ye, and let us go up to the mountain of the Lord , to the house of the God of Jacob; and he will teach us of his ways, and we will walk in his paths: for out of Zion shall go forth the law, and the word of the Lord from Jerusalem. [4] And he shall judge among the nations, and shall rebuke many people: and they shall beat their swords into plowshares, and their spears into pruninghooks: nation shall not lift up sword against nation, neither shall they learn war any more. [5] O house of Jacob, come ye, and let us walk in the light of the Lord .
Jesus gave this commission to the church:
Matthew 28:18-20 KJV
And Jesus came and spake unto them, saying, All power is given unto me in heaven and in earth. [19] Go ye therefore, and teach all nations, baptizing them in the name of the Father, and of the Son, and of the Holy Ghost: [20] Teaching them to observe all things whatsoever I have commanded you: and, lo, I am with you alway, even unto the end of the world. Amen.
Ephesians 3:7-11 KJV
Whereof I was made a minister, according to the gift of the grace of God given unto me by the effectual working of his power. [8] Unto me, who am less than the least of all saints, is this grace given, that I should preach among the Gentiles the unsearchable riches of Christ; [9] And to make all men see what is the fellowship of the mystery, which from the beginning of the world hath been hid in God, who created all things by Jesus Christ: [10] To the intent that now unto the principalities and powers in heavenly places might be known by the church the manifold wisdom of God, [11] According to the eternal purpose which he purposed in Christ Jesus our Lord:
This includes the 4th commandment:
Isaiah 56:1-8 KJV
Thus saith the Lord , Keep ye judgment, and do justice: for my salvation is near to come, and my righteousness to be revealed. [2] Blessed is the man that doeth this, and the son of man that layeth hold on it; that keepeth the sabbath from polluting it, and keepeth his hand from doing any evil. [3] Neither let the son of the stranger, that hath joined himself to the Lord , speak, saying, The Lord hath utterly separated me from his people: neither let the eunuch say, Behold, I am a dry tree. [4] For thus saith the Lord unto the eunuchs that keep my sabbaths, and choose the things that please me, and take hold of my covenant; [5] Even unto them will I give in mine house and within my walls a place and a name better than of sons and of daughters: I will give them an everlasting name, that shall not be cut off. [6] Also the sons of the stranger, that join themselves to the Lord , to serve him, and to love the name of the Lord , to be his servants, every one that keepeth the sabbath from polluting it, and taketh hold of my covenant; [7] Even them will I bring to my holy mountain, and make them joyful in my house of prayer: their burnt offerings and their sacrifices shall be accepted upon mine altar; for mine house shall be called an house of prayer for all people. [8] The Lord God which gathereth the outcasts of Israel saith, Yet will I gather others to him, beside those that are gathered unto him.