"In declaring that one man should die for the nation, Caiaphas indicated that he had some knowledge of the prophecies, although it was very limited. But John, in his account of this scene, takes up the prophecy, and shows its broad and deep significance. He says, “And not for that nation only, but that also He should gather together in one the children of God that were scattered abroad.” How blindly did the haughty Caiaphas acknowledge the Saviour's mission! DA 540.1"
"And not for that nation only, but that also he should gather together in one the children of God that were scattered abroad."
The EGW passage directly quotes and interprets John 11:52, making it an explicit allusion.
"reasoning he thought to silence the remonstrances of those who might dare to say that as yet nothing worthy of death had been found in Jesus. DA 540.2"
"If we let him thus alone, all men will believe on him: and the Romans shall come and take away both our place and nation."
Both passages deal with the fear of the Jewish leaders that Jesus's popularity will lead to Roman intervention. The EGW passage provides an interpretation of the leaders' motives, which is thematically linked to the concerns expressed in John 11:48.
"At this council Christ's enemies had been deeply convicted. The Holy Spirit had impressed their minds. But Satan strove to gain control of them. He urged upon their notice the grievances they had suffered on account of Christ. How little He had honored their righteousness. He presented a righteousness far greater, which all who would be children of God must possess. Taking no notice of their forms and ceremonies, He had encouraged sinners to go directly to God as a merciful Father, and make known their wants. Thus, in their opinion, He had set aside the priesthood. He had refused to acknowledge the theology of the rabbinical schools. He had exposed the evil practices of the priests, and had irreparably hurt their influence. He had injured the effect of their maxims and traditions, declaring that though they strictly enforced the ritual law, they made void the law of God. All this Satan now brought to their minds. DA 540.3"
"Even so ye also outwardly appear righteous unto men, but within ye are full of hypocrisy and iniquity."
The EGW passage describes the hypocrisy of the priests, which is a central theme in Matthew 23, including verse 28.
"How can ye believe, which receive honour one of another, and seek not the honour that cometh from God only?"
The EGW passage discusses the priests' concern for their own honor and influence, which aligns with the theme of seeking honor from men rather than from God in John 5:44.