"The Messenger of heaven replied, “Go in this thy might, and thou shalt save Israel from the hand of the Midianites: have not I sent thee?” PP 547.1"
"And the Lord looked upon him, and said, Go in this thy might, and thou shalt save Israel from the hand of the Midianites: have not I sent thee?"
This is a direct quote from Judges 6:14, making it a clear and undeniable explicit allusion.
"Gideon desired some token that the one now addressing him was the Covenant Angel, who in time past had wrought for Israel. Angels of God, who communed with Abraham, had once tarried to share his hospitality; and Gideon now entreated the divine Messenger to remain as his guest. Hastening to his tent, he prepared from his scanty store a kid and unleavened cakes, which he brought forth and set before Him. But the Angel bade him, “Take the flesh and the unleavened cakes, and lay them upon this rock, and pour out the broth.” Gideon did so, and then the sign which he had desired was given: with the staff in His hand, the Angel touched the flesh and the unleavened cakes, and a flame bursting from the rock consumed the sacrifice. Then the Angel vanished from his sight. PP 547.2"
"Depart not hence, I pray thee, until I come unto thee, and bring forth my present, and set it before thee. And he said, I will tarry until thou come again."
EGW recounts the story of Gideon's offering and the Angel's response, directly referencing events described in Judges 6, including the request to tarry and the offering of food.
"present a sacrifice to the Lord. The offering of sacrifice to God had been committed to the priests, and had been restricted to the altar at Shiloh; but He who had established the ritual service, and to whom all its offerings pointed, had power to change its requirements. The deliverance of Israel was to be preceded by a solemn protest against the worship of Baal. Gideon must declare war upon idolatry before going out to battle with the enemies of his people. PP 547.3"
"And it came to pass the same night, that the Lord said unto him, Take thy father’s young bullock, even the second bullock of seven years old, and throw down the altar of Baal that thy father hath, and cut down the grove that is by it:"
EGW directly references Gideon's instruction to destroy the altar of Baal, which is described in Judges 6:25. The connection is clear and explicit.
"The divine direction was faithfully carried out. Knowing that he would be opposed if it were attempted openly, Gideon performed the work in secret; with the aid of his servants, accomplishing the whole in one night. Great was the rage of the men of Ophrah when they came next morning to pay their devotions to Baal. They would have taken Gideon's life had not Joash—who had been told of the Angel's visit—stood in defense of his son. “Will ye plead for Baal?” said Joash. “Will ye save him? he that will plead for him, let him be put to death whilst it is yet morning: if he be a god, let him plead for himself, because one hath cast down his altar.” If Baal could not defend his own altar, how could he be trusted to protect his worshipers? PP 547.4"
"Then Gideon took ten men of his servants, and did as the Lord had said unto him: and so it was, because he feared his father’s household, and the men of the city, that he could not do it by day, that he did it by night."
The EGW passage directly recounts and expands upon the events described in Judges 6:27, including Gideon's actions and Joash's defense of his son.