"The evening was pleasant, and Peter, who still had much of his old love for boats and fishing, proposed that they should go out upon the sea and cast their nets. In this plan all were ready to join; they were in need of food and clothing, which the proceeds of a successful night's fishing would supply. So they went out in their boat, but they caught nothing. All night they toiled, without success. Through the weary hours they talked of their absent Lord, and recalled the wonderful events they had witnessed in His ministry beside the sea. They questioned as to their own future, and grew sad at the prospect before them. DA 810.1"
"Simon Peter saith unto them, I go a fishing. They say unto him, We also go with thee. They went forth, and entered into a ship immediately; and that night they caught nothing."
The EGW passage closely follows the narrative of John 21:3, describing the disciples' decision to go fishing, their lack of success, and their reflections on Jesus.
"therefore, and now they were not able to draw it for the multitude of fishes.” DA 810.2"
"And he said unto them, Cast the net on the right side of the ship, and ye shall find. They cast therefore, and now they were not able to draw it for the multitude of fishes."
This is a direct quote from John 21:6, making it a clear and undeniable explicit allusion.
"John recognized the stranger, and exclaimed to Peter, “It is the Lord.” Peter was so elated and so glad that in his eagerness he cast himself into the water and was soon standing by the side of his Master. The other disciples came in their boat, dragging the net with fishes. “As soon then as they were come to land, they saw a fire of coals there, and fish laid thereon, and bread.” DA 810.3"
"Therefore that disciple whom Jesus loved saith unto Peter, It is the Lord. Now when Simon Peter heard that it was the Lord, he girt his fisher’s coat unto him, (for he was naked,) and did cast himself into the sea."
The EGW passage directly recounts the events of John 21:7, including John's recognition of Jesus, Peter's reaction, and the disciples' arrival on shore with the fish. It's a very close paraphrase.
"They were too much amazed to question whence came the fire and the food. “Jesus saith unto them, Bring of the fish which ye have now caught.” Peter rushed for the net, which he had dropped, and helped his brethren drag it to the shore. After the work was done, and the preparation made, Jesus bade the disciples come and dine. He broke the food, and divided it among them, and was known and acknowledged by all the seven. The miracle of feeding the five thousand on the mountainside was now brought to their minds; but a mysterious awe was upon them, and in silence they gazed upon the risen Saviour. DA 810.4"
"Jesus saith unto them, Come and dine. And none of the disciples durst ask him, Who art thou? knowing that it was the Lord."
The EGW passage retells the event in John 21:12, adding details and interpretations. The core event of Jesus inviting the disciples to dine is central to both passages.
Vividly they recalled the scene beside the sea when Jesus had bidden them follow Him. They remembered how, at His command, they had launched out into the deep, and had let down their net, and the catch had been so abundant as to fill the net, even to breaking. Then Jesus had called them to leave their fishing boats, and had promised to make them fishers of men. It was to bring this scene to their minds, and to deepen its impression, that He had again performed the miracle. His act was a renewal of the commission to the disciples. It showed them that the death of their Master had not lessened their obligation to do the work He had assigned them. Though they were to be deprived of His personal companionship, and of the means of support by their former employment, the risen Saviour would still have a care for them. While they were doing His work, He would provide for their needs. And Jesus had a purpose in bidding them cast their net on the right side of the ship. On that side He stood up…
"Now when he had left speaking, he said unto Simon, Launch out into the deep, and let down your nets for a draught. And Simon answering said unto him, Master, we have toiled all the night, and have taken nothing: nevertheless at thy word I will let down the net. And when they had this done, they inclosed a great multitude of fishes: and their net brake. And they beckoned unto their partners, which were in the other ship, that they should come and help them. And they came, and filled both the ships, so that they began to sink. When Simon Peter saw it, he fell down at Jesus’ knees, saying, Depart from me; for I am a sinful man, O Lord. For he was astonished, and all that were with him, at the draught of the fishes which they had taken: And so was also James, and John, the sons of Zebedee, which were partners with Simon. And Jesus said unto Simon, Fear not; from henceforth thou shalt catch men. And when they had brought their ships to land, they forsook all, and followed him."
The EGW passage explicitly refers to and interprets the earlier fishing miracle in Luke 5:4-11, drawing parallels and highlighting its significance in the context of the post-resurrection appearance. It's a clear and intentional allusion.