"Caring for the Sick We returned home from this tour just before a great fall of rain which carried off the snow. This storm prevented the next Sabbath meeting, and I immediately commenced to prepare matter for Testimony No. 14. We also had the privilege of caring for our dear Brother Seneca King, whom we brought to our home with a terrible injury upon the head and face. We took him to our house to die, for we could not think it possible for one with the skull so terribly broken in to recover. But with the blessing of God upon a very gentle use of water, a very spare diet till the danger of fever was past, and well ventilated rooms day and night, in three weeks he was able to return to his home and attend to his farming interests. He did not take one grain of medicine from first to last. Although he was considerably reduced by loss of blood from his wounds and by spare diet, yet when he could take a more liberal amount of food he came up rapidly. LS 185"
"And the King shall answer and say unto them, Verily I say unto you, Inasmuch as ye have done it unto one of the least of these my brethren, ye have done it unto me."
The EGW passage describes caring for a sick brother, which aligns with the principle of Matthew 25:40 about caring for 'the least of these'. The act of service and care is the key connection.
"At Tittabawassee we found a large house of worship recently built by our people, well filled with Sabbath keepers. The brethren seemed ready for our testimony, and we enjoyed freedom. The next day fifteen were baptized. LS 185.1"
"Then they that gladly received his word were baptized: and the same day there were added unto them about three thousand souls."
Both passages describe a successful preaching event followed by baptisms. While the scale differs greatly, the thematic parallel of preaching leading to baptism is present.
"At Vassar we held our meetings Sabbath and first day at the union schoolhouse. This was a free place in which to speak, and we saw good fruit of our labors. First day afternoon about thirty backsliders, and children who had made no profession, came forward for prayers. LS 185.2"
"Confess your faults one to another, and pray one for another, that ye may be healed. The effectual fervent prayer of a righteous man availeth much."
The EGW passage describes people coming forward for prayer, including backsliders, which aligns with the James 5:16 call to confess faults and pray for one another. The connection is that prayer is sought for healing and restoration.