"Overwhelmed with sorrow, Nehemiah could neither eat nor drink; he “wept, and mourned certain days, and fasted.” In his grief he turned to the divine Helper. “I ... prayed,” he said, “before the God of heaven.” Faithfully he made confession of his sins and the sins of his people. He pleaded that God would maintain the cause of Israel, restore their courage and strength, and help them to build up the waste places of Judah. PK 629.1"
"And it came to pass, when I heard these words, that I sat down and wept, and mourned certain days, and fasted, and prayed before the God of heaven,"
EGW directly quotes and references Nehemiah 1:4, describing Nehemiah's reaction to the news of Jerusalem's state.
"And I prayed unto the Lord my God, and made my confession, and said, O Lord, the great and dreadful God, keeping the covenant and mercy to them that love him, and to them that keep his commandments;"
Both passages describe prayer and confession of sins. While not a direct quote, the theme of confession is present in both.
"As Nehemiah prayed, his faith and courage grew strong. His mouth was filled with holy arguments. He pointed to the dishonor that would be cast upon God, if His people, now that they had returned to Him, should be left in weakness and oppression; and he urged the Lord to bring to pass His promise: “If ye turn unto Me, and keep My Commandments, and do them; though there were of you cast out unto the uttermost part of the heaven, yet will I gather them from thence, and will bring them unto the place that I have chosen to set My name there.” See Deuteronomy 4:29-31 . This promise had been given to Israel through Moses before they had entered Canaan, and during the centuries it had stood unchanged. God's people had now returned to Him in penitence and faith, and His promise would not fail. PK 629.2"
"But if from thence thou shalt seek the Lord thy God, thou shalt find him, if thou seek him with all thy heart and with all thy soul. When thou art in tribulation, and all these things are come upon thee, even in the latter days, if thou turn to the Lord thy God, and shalt be obedient unto his voice; (For the Lord thy God is a merciful God;) he will not forsake thee, neither destroy thee, nor forget the covenant of thy fathers which he sware unto them."
Ellen White directly references Deuteronomy 4:29-31 in this passage.
"If any of thine be driven out unto the outmost parts of heaven, from thence will the Lord thy God gather thee, and from thence will he fetch thee:"
EGW directly quotes Deuteronomy 30:4, highlighting the promise of God gathering His people from the uttermost parts of heaven.
"And shalt return unto the Lord thy God, and shalt obey his voice according to all that I command thee this day, thou and thy children, with all thine heart, and with all thy soul;"
Both passages discuss returning to God and obeying His voice. EGW references Deuteronomy 4:29-31, but the provided verse is thematically similar.