The demands upon God are even greater upon the Sabbath than upon other days. His people then leave their usual employment, and spend the time in meditation and worship. They ask more favors of Him on the Sabbath than upon other days. They demand His special attention. They crave His choicest blessings. God does not wait for the Sabbath to pass before He grants these requests. Heaven's work never ceases, and men should never rest from doing good. The Sabbath is not intended to be a period of useless inactivity. The law forbids secular labor on the rest day of the Lord; the toil that gains a livelihood must cease; no labor for worldly pleasure or profit is lawful upon that day; but as God ceased His labor of creating, and rested upon the Sabbath and blessed it, so man is to leave the occupations of his daily life, and devote those sacred hours to healthful rest, to worship, and to holy deeds. The work of Christ in healing the sick was in perfect accord with the law. It honored the Sabbat…
"How much then is a man better than a sheep? Wherefore it is lawful to do well on the sabbath days."
Both passages address the permissibility of doing good on the Sabbath. Matthew 12:12 explicitly states "it is lawful to do well on the sabbath days," and EGW argues that Christ's healing was in accordance with the law and that the Sabbath is not intended for useless inactivity, but for holy deeds.
"Therefore the Jews sought the more to kill him, because he not only had broken the sabbath, but said also that God was his Father, making himself equal with God."
Ellen White directly references John 5:18 in this passage.
"The whole nation of the Jews called God their Father, therefore they would not have been so enraged if Christ had represented Himself as standing in the same relation to God. But they accused Him of blasphemy, showing that they understood Him as making this claim in the highest sense. DA 207.4"
"Therefore the Jews sought the more to kill him, because he not only had broken the sabbath, but said also that God was his Father, making himself equal with God."
The EGW passage directly references and interprets the events described in John 5:18, specifically the Jews' reaction to Jesus calling God his Father.