"Saul was in disfavor with God, and yet unwilling to humble his heart in penitence. What he lacked in real piety he would try to make up by his zeal in the forms of religion. Saul was not ignorant of Israel's defeat when the ark of God was brought into the camp by Hophni and Phinehas; and yet, knowing all this, he determined to send for the sacred chest and its attendant priest. Could he by this means inspire confidence in the people, he hoped to reassemble his scattered army and give battle to the Philistines. He would now dispense with Samuel's presence and support, and thus free himself from the prophet's unwelcome criticisms and reproofs. PP 622.1"
"And when the people were come into the camp, the elders of Israel said, Wherefore hath the Lord smitten us to day before the Philistines? Let us fetch the ark of the covenant of the Lord out of Shiloh unto us, that, when it cometh among us, it may save us out of the hand of our enemies."
Both passages describe a situation where the Israelites, facing defeat, attempt to use the Ark of the Covenant as a means to regain confidence and victory. This is a clear thematic parallel.
"history of Israel's first king presents a sad example of the power of early wrong habits. In his youth Saul did not love and fear God; and that impetuous spirit, not early trained to submission, was ever ready to rebel against divine authority. Those who in their youth cherish a sacred regard for the will of God, and who faithfully perform the duties of their position, will be prepared for higher service in afterlife. But men cannot for years pervert the powers that God has given them, and then, when they choose to change, find these powers fresh and free for an entirely opposite course. PP 622.2"
"Train up a child in the way he should go: and when he is old, he will not depart from it."
The EGW passage directly applies the principle of Proverbs 22:6 regarding the importance of early training and its lasting impact on character and future actions.
"Saul's efforts to arouse the people proved unavailing. Finding his force reduced to six hundred men, he left Gilgal and retired to the fortress at Geba, lately taken from the Philistines. This stronghold was on the south side of a deep, rugged valley, or gorge, a few miles north of the site of Jerusalem. On the north side of the same valley, at Michmash, the Philistine force lay encamped while detachments of troops went out in different directions to ravage the country. PP 622.3"
"When the men of Israel saw that they were in a strait, (for the people were distressed,) then the people did hide themselves in caves, and in thickets, and in rocks, and in high places, and in pits."
While not a direct quote, the EGW passage describes the dire situation of the Israelites and the Philistine encampment, which is the context for 1 Samuel 13:6. The people hiding in caves is a consequence of the events described by EGW.