"Elijah should not have fled from his post of duty. He should have met the threat of Jezebel with an appeal for protection to the One who had commissioned him to vindicate the honor of Jehovah. He should have told the messenger that the God in whom he trusted would protect him against the hatred of the queen. Only a few hours had passed since he had witnessed a wonderful manifestation of divine power, and this should have given him assurance that he would not now be forsaken. Had he remained where he was, had he made God his refuge and strength, standing steadfast for the truth, he would have been shielded from harm. The Lord would have given him another signal victory by sending His judgments on Jezebel; and the impression made on the king and the people would have wrought a great reformation. PK 160.1"
"God is our refuge and strength, a very present help in trouble."
The EGW passage directly applies the principle of trusting in God as a refuge and strength, which is explicitly stated in Psalm 46:1. EGW uses the verse's concept to critique Elijah's actions.
"Elijah had expected much from the miracle wrought on Carmel. He had hoped that after this display of God's power, Jezebel would no longer have influence over the mind of Ahab, and that there would be a speedy reform throughout Israel. All day on Carmel's height he had toiled without food. Yet when he guided the chariot of Ahab to the gate of Jezreel, his courage was strong, despite the physical strain under which he had labored. PK 160.2"
"And Elijah said unto Ahab, Get thee up, eat and drink; for there is a sound of abundance of rain."
Both passages refer to Elijah's interaction with Ahab after the events on Mount Carmel. While EGW focuses on Elijah's expectations and physical state, and 1 Kings 18:41 records Elijah telling Ahab to eat and drink, there is a thematic connection in that both passages describe the immediate aftermath of the Carmel events and Elijah's continued involvement. It's not a strong connection, but it's present.