"Chapter 8—The Ministry of John The apostle John passed his early life in the society of the uncultivated fishermen of Galilee. He did not enjoy the training of the schools; but by association with Christ, the Great Teacher, he obtained the highest education which mortal man can receive. He drank eagerly at the fountain of wisdom, and then sought to lead others to that “well of water springing up into everlasting life” ( John 4:14 ). The simplicity of his words, the sublime power of the truths he uttered, and the spiritual fervor that characterized his teachings gave him access to all classes. Yet even believers were unable to fully comprehend the sacred mysteries of divine truth unfolded in his discourses. He seemed to be constantly imbued with the Holy Spirit. He sought to bring the thoughts of the people up to grasp the unseen. The wisdom with which he spoke, caused his words to drop as the dew, softening and subduing the soul. SL 61"
"But whosoever drinketh of the water that I shall give him shall never thirst; but the water that I shall give him shall be in him a well of water springing up into everlasting life."
Ellen White directly references John 4:14 in this passage.
"After the ascension of Christ, John stands forth a faithful, ardent laborer for the Master. With others he enjoyed the outpouring of the Spirit on the day of Pentecost, and with fresh zeal and power he continued to speak to the people the words of life. He was threatened with imprisonment and death, but he would not be intimidated. SL 61.2"
"Now when they saw the boldness of Peter and John, and perceived that they were unlearned and ignorant men, they marvelled; and they took knowledge of them, that they had been with Jesus."
Both passages highlight John's boldness and association with Peter after the ascension. While the EGW passage focuses on his zeal and power, Acts 4:13 mentions the observation of his boldness and recognition of his association with Jesus. There is a clear thematic connection.
"Then Peter and the other apostles answered and said, We ought to obey God rather than men."
Both passages deal with the theme of obedience to God versus obedience to human authority. The EGW passage mentions John's refusal to be intimidated by threats, while Acts 5:29 explicitly states the principle of obeying God rather than men. The connection is thematic, though not a direct quote or allusion.