"The apostle knew that he could not look for justice from the people who by their crimes were bringing down upon themselves the wrath of God. He knew that, like the prophet Elijah, he would be safer among the heathen than with those who had rejected light from heaven and hardened their hearts against the gospel. Weary of strife, his active spirit could ill endure the repeated delays and wearing suspense of his trial and imprisonment. He therefore decided to exercise his privilege, as a Roman citizen, of appealing to Caesar. AA 430.1"
"And when he saw that, he arose, and went for his life, and came to Beer–sheba, which belongeth to Judah, and left his servant there."
Both Elijah and Paul sought safety among those who were not their own people due to threats from their own. The parallel is that both prophets sought refuge from danger, though the circumstances differ.
"In answer to the governor's question, Paul said: “I stand at Caesar's judgment seat, where I ought to be judged: to the Jews have I done no wrong, as thou very well knowest. For if I be an offender, or have committed anything worthy of death, I refuse not to die: but if there be none of these things whereof these accuse me, no man may deliver me unto them. I appeal unto Caesar.” AA 430.2"
"Then said Paul, I stand at Cesar’s judgment seat, where I ought to be judged: to the Jews have I done no wrong, as thou very well knowest."
This is a direct quote from Acts 25:10.
"Festus knew nothing of the conspiracies of the Jews to murder Paul, and he was surprised at this appeal to Caesar. However, the words of the apostle put a stop to the proceedings of the court. “Festus, when he had conferred with the council, answered, Hast thou appealed unto Caesar? unto Caesar shalt thou go.” AA 430.3"
"Then Festus, when he had conferred with the council, answered, Hast thou appealed unto Cesar? unto Cesar shalt thou go."
This is a direct quote from Acts 25:12.
"Thus it was that once more, because of hatred born of bigotry and self-righteousness, a servant of God was driven to turn for protection to the heathen. It was this same hatred that forced the prophet Elijah to flee for succor to the widow of Sarepta; and that forced the heralds of the gospel to turn from the Jews to proclaim their message to the Gentiles. And this hatred the people of God living in this age have yet to meet. Among many of the professing followers of Christ there is the same pride, formalism, and selfishness, the same spirit of oppression, that held so large a place in the Jewish heart. In the future, men claiming to be Christ's representatives will take a course similar to that followed by the priests and rulers in their treatment of Christ and the apostles. In the great crisis through which they are soon to pass, the faithful servants of God will encounter the same hardness of heart, the same cruel determination, the same unyielding hatred. AA 430.4"
"Arise, get thee to Zarephath, which belongeth to Zidon, and dwell there: behold, I have commanded a widow woman there to sustain thee."
EGW uses the example of Elijah fleeing to the widow of Sarepta as an example of God's servants seeking protection from those who hate them, which is a valid thematic parallel to the broader narrative in 1 Kings 17:9.