"No sooner does the child of God approach the mercy seat than he becomes the client of the great Advocate. At his first utterance of penitence and appeal for pardon Christ espouses his case and makes it His own, presenting the supplication before the Father as His own request. 6T 364.1"
"Let us therefore come boldly unto the throne of grace, that we may obtain mercy, and find grace to help in time of need."
Both passages deal with approaching God's throne for mercy and grace. EGW expands on the idea of Christ as an advocate, which is implicit in Hebrews 4:16.
"My little children, these things write I unto you, that ye sin not. And if any man sin, we have an advocate with the Father, Jesus Christ the righteous:"
Both passages explicitly mention Jesus as an advocate. EGW's statement directly echoes the concept of Christ as an advocate presented in 1 John 2:1.
"As Christ intercedes in our behalf, the Father lays open all the treasures of His grace for our appropriation, to be enjoyed and to be communicated to others. “Ask in My name,” Christ says; “I do not say that I will pray the Father for you; for the Father Himself loveth you, because you have loved Me. Make use of My name. This will give your prayers efficiency, and the Father will give you the riches of His grace; wherefore, ‘ask, and ye shall receive, that your joy may be full.’” John 16:24 . 6T 364.2"
"Hitherto have ye asked nothing in my name: ask, and ye shall receive, that your joy may be full."
EGW directly quotes John 16:24 within the passage, making it an explicit allusion.
"And whatsoever ye shall ask in my name, that will I do, that the Father may be glorified in the Son."
EGW's passage discusses asking in Christ's name and receiving grace, which is the central theme of John 14:13. While not a direct quote, the concept is clearly linked.
The dealings of God with His people should be often repeated. How frequently were the waymarks set up by the Lord in His dealings with ancient Israel! Lest they should forget the history of the past, He commanded Moses to frame these events into song, that parents might teach them to their children. They were to gather up memorials and to lay them up in sight. Special pains were taken to preserve them, that when the children should inquire concerning these things, the whole story might be repeated. Thus the providential dealings and the marked goodness and mercy of God in His care and deliverance of His people were kept in mind. We are exhorted to call to “remembrance the former days, in which, after ye were illuminated, ye endured a great fight of afflictions.” Hebrews 10:32 . For His people in this generation the Lord has wrought as a wonder-working God. The past history of the cause of God needs to be often brought before the people, young and old. We need often to recount God's goo…
"But call to remembrance the former days, in which, after ye were illuminated, ye endured a great fight of afflictions;"
Ellen White directly references Hebrews 10:32 in this passage.