"“The Lord said unto Satan, The Lord rebuke thee, O Satan, even the Lord that hath chosen Jerusalem rebuke thee: is not this a brand plucked out of the fire?” When Satan seeks to cover the people of God with blackness, and ruin them, Christ interposes. Although they have sinned, Christ has taken the guilt of their sins upon His own soul. He has snatched the race as a brand from the fire. By His human nature He is linked with man, while through His divine nature He is one with the infinite God. Help is brought within the reach of perishing souls. The adversary is rebuked. COL 169.1"
"And the Lord said unto Satan, The Lord rebuke thee, O Satan; even the Lord that hath chosen Jerusalem rebuke thee: is not this a brand plucked out of the fire?"
EGW directly quotes and expands upon Zechariah 3:2, applying it to Christ's intercession for humanity.
"“Now Joshua was clothed with filthy garments, and stood before the angel: and he answered and spake unto those that stood before him, saying, Take away the filthy garments from him. And unto him he said, Behold, I have caused thine iniquity to pass from thee, and I will clothe thee with change of raiment. And I said, Let them set a fair miter upon his head. So they set a fair miter upon his head, and clothed him with garments.” Then with the authority of the Lord of hosts the angel made a solemn pledge to Joshua, the representative of God's people: “If thou wilt walk in My ways, and if thou wilt keep My charge, then thou shalt also judge My house, and shalt also keep My courts, and I will give thee places to walk among these that stand by”—even among the angels that surround the throne of God. ( Zechariah 3:3-7 .) COL 169.2"
"Now Joshua was clothed with filthy garments, and stood before the angel. And he answered and spake unto those that stood before him, saying, Take away the filthy garments from him. And unto him he said, Behold, I have caused thine iniquity to pass from thee, and I will clothe thee with change of raiment. And I said, Let them set a fair mitre upon his head. So they set a fair mitre upon his head, and clothed him with garments. And the angel of the Lord stood by. And the angel of the Lord protested unto Joshua, saying, Thus saith the Lord of hosts; If thou wilt walk in my ways, and if thou wilt keep my charge, then thou shalt also judge my house, and shalt also keep my courts, and I will give thee places to walk among these that stand by."
Ellen White directly references Zechariah 3:3-7 in this passage.
"Notwithstanding the defects of the people of God, Christ does not turn away from the objects of His care. He has the power to change their raiment. He removes the filthy garments, He places upon the repenting, believing ones His own robe of righteousness, and writes pardon against their names on the records of heaven. He confesses them as His before the heavenly universe. Satan their adversary is shown to be an accuser and deceiver. God will do justice for His own elect. COL 169.3"
"And he answered and spake unto those that stood before him, saying, Take away the filthy garments from him. And unto him he said, Behold, I have caused thine iniquity to pass from thee, and I will clothe thee with change of raiment."
Both passages speak of removing filthy garments and clothing with new raiment, representing forgiveness and righteousness. The connection is strong and meaningful.
"He that overcometh, the same shall be clothed in white raiment; and I will not blot out his name out of the book of life, but I will confess his name before my Father, and before his angels."
Both passages discuss being clothed in white raiment and having one's name confessed before God. The connection is clear and relevant.
"Who shall lay any thing to the charge of God’s elect? It is God that justifieth."
Both passages refer to God's elect and the concept of justification. While the connection is present, it's less direct than the previous examples.