"This instance was to be a lesson to all Israel to the close of time that God is the strength of His people. When Israel triumphed, Moses was reaching his hands toward heaven and interceding in their behalf; so when all the Israel of God prevail, it is because the Mighty One undertakes their case and fights their battles for them. Moses did not ask or believe that God would overcome their foes while Israel remained inactive. He marshals all his forces and sends them out as well prepared as their facilities can make them, and then he takes the whole matter to God in prayer. Moses on the mount is pleading with the Lord, while Joshua with his brave followers is below, doing his best to meet and repulse the enemies of Israel and of God. 4T 531.1"
"And it came to pass, when Moses held up his hand, that Israel prevailed: and when he let down his hand, Amalek prevailed."
The EGW passage draws a direct principle from the Exodus 17:11 account, stating that God is the strength of His people and that their success depends on His intervention, mirroring Moses' intercession.
"That prayer which comes forth from an earnest, believing heart is the effectual, fervent prayer that availeth much. God does not always answer our prayers as we expect, for we may not ask what would be for our highest good; but in His infinite love and wisdom He will give us those things which we most need. Happy the minister who has a faithful Aaron and Hur to strengthen his hands when they become weary and to hold them up by faith and prayer. Such a support is a powerful aid to the servant of Christ in his work and will often make the cause of truth to triumph gloriously. 4T 531.2"
"Confess your faults one to another, and pray one for another, that ye may be healed. The effectual fervent prayer of a righteous man availeth much."
The EGW passage directly quotes and applies James 5:16, making it an explicit allusion. The reference to Aaron and Hur is also a thematic connection to the previous verses.
"If ye then, being evil, know how to give good gifts unto your children, how much more shall your Father which is in heaven give good things to them that ask him?"
Both passages deal with the idea that God answers prayers and provides what is needed, even if it's not exactly what is asked for. The connection is thematic, focusing on God's provision in response to prayer.
"After the transgression of Israel in making the golden calf, Moses again goes to plead with God in behalf of his people. He has some knowledge of those who have been placed under his care; he knows the perversity of the human heart and realizes the difficulties with which he must contend. But he has learned from experience that in order to have an influence with the people he must first have power with God. The Lord reads the sincerity and unselfish purpose of the heart of His servant and condescends to commune with this feeble mortal, face to face, as a man speaks with a friend. Moses casts himself and all his burdens fully upon God and freely pours out his soul before Him. The Lord does not reprove His servant, but stoops to listen to his supplications. 4T 531.3"
"And it came to pass on the morrow, that Moses said unto the people, Ye have sinned a great sin: and now I will go up unto the Lord; peradventure I shall make an atonement for your sin. And Moses returned unto the Lord, and said, Oh, this people have sinned a great sin, and have made them gods of gold. Yet now, if thou wilt forgive their sin—; and if not, blot me, I pray thee, out of thy book which thou hast written."
Both passages describe Moses interceding with God on behalf of the Israelites after the golden calf incident. The EGW passage elaborates on Moses' role and relationship with God in this context, drawing a thematic parallel to the biblical narrative.