"Chapter 53—John the Beloved John is distinguished above the other apostles as “the disciple whom Jesus loved.” John 21:20 . He seems to have enjoyed to a pre-eminent degree the friendship of Christ, and he received many tokens of the Saviour's confidence and love. He was one of the three permitted to witness Christ's glory upon the mount of transfiguration and His agony in Gethsemane, and it was to his care that our Lord confided His mother in those last hours of anguish upon the cross. AA 539"
"Then Peter, turning about, seeth the disciple whom Jesus loved following; which also leaned on his breast at supper, and said, Lord, which is he that betrayeth thee?"
Ellen White directly references John 21:20 in this passage.
"The Saviour's affection for the beloved disciple was returned with all the strength of ardent devotion. John clung to Christ as the vine clings to the stately pillar. For his Master's sake he braved the dangers of the judgment hall and lingered about the cross, and at the tidings that Christ had risen, he hastened to the sepulcher, in his zeal out-stripping even the impetuous Peter. AA 539.2"
"When Jesus therefore saw his mother, and the disciple standing by, whom he loved, he saith unto his mother, Woman, behold thy son!"
The EGW passage describes John's devotion to Jesus, which is exemplified in John 19:26 where he is present at the crucifixion and referred to as 'the disciple whom he loved.' While not a direct quote, it reflects the same theme.
"The confiding love and unselfish devotion manifested in the life and character of John present lessons of untold value to the Christian church. John did not naturally possess the loveliness of character that his later experience revealed. By nature he had serious defects. He was not only proud, self-assertive, and ambitious for honor, but impetuous, and resentful under injury. He and his brother were called “sons of thunder.” Evil temper, the desire for revenge, the spirit of criticism, were all in the beloved disciple. But beneath all this the divine Teacher discerned the ardent, sincere, loving heart. Jesus rebuked this self-seeking, disappointed his ambitions, tested his faith. But He revealed to him that for which his soul longed—the beauty of holiness, the transforming power of love. AA 539.3"
"And James the son of Zebedee, and John the brother of James; and he surnamed them Boanerges, which is, The sons of thunder:"
The EGW passage directly references Mark 3:17 and the nickname 'sons of thunder' given to James and John.
"And when his disciples James and John saw this, they said, Lord, wilt thou that we command fire to come down from heaven, and consume them, even as Elias did?"
The EGW passage refers to the event in Luke 9:54 where James and John ask Jesus if they should call down fire from heaven.