"Above all others the priests and rulers should have seen in Jesus the anointed of the Lord; for in their hands were the sacred scrolls that described His mission, and they knew that the cleansing of the temple was a manifestation of more than human power. Much as they hated Jesus, they could not free themselves from the thought that He might be a prophet sent by God to restore the sanctity of the temple. With a deference born of this fear, they went to Him with the inquiry, “What sign showest Thou unto us, seeing that Thou doest these things?” DA 164.1"
"Search the scriptures; for in them ye think ye have eternal life: and they are they which testify of me."
Both passages highlight the importance of the scriptures in recognizing Jesus as the Messiah. The EGW passage directly states that the priests and rulers should have seen Jesus in the scriptures, echoing the sentiment in John 5:39.
"Jesus had shown them a sign. In flashing light into their hearts, and in doing before them the works which the Messiah was to do, He had given convincing evidence of His character. Now when they asked for a sign, He answered them by a parable, showing that He read their malice, and saw to what lengths it would lead them. “Destroy this temple,” He said, “and in three days I will raise it up.” DA 164.2"
"Jesus answered and said unto them, Destroy this temple, and in three days I will raise it up."
The EGW passage directly quotes and interprets John 2:19, making it a clear and explicit allusion.
"In these words His meaning was twofold. He referred not only to the destruction of the Jewish temple and worship, but to His own death,—the destruction of the temple of His body. This the Jews were already plotting. As the priests and rulers returned to the temple, they had proposed to kill Jesus, and thus rid themselves of the troubler. Yet when He set before them their purpose, they did not understand Him. They took His words as applying only to the temple at Jerusalem, and with indignation exclaimed, “Forty and six years was this temple in building, and wilt Thou rear it up in three days?” Now they felt that Jesus had justified their unbelief, and they were confirmed in their rejection of Him. DA 164.3"
"Then said the Jews, Forty and six years was this temple in building, and wilt thou rear it up in three days?"
The EGW passage directly quotes and interprets John 2:20, making it a clear and explicit allusion.
"Christ did not design that His words should be understood by the unbelieving Jews, nor even by His disciples at this time. He knew that they would be misconstrued by His enemies, and would be turned against Him. At His trial they would be brought as an accusation, and on Calvary they would be flung at Him as a taunt. But to explain them now would give His disciples a knowledge of His sufferings, and bring upon them sorrow which as yet they were not able to bear. And an explanation would prematurely disclose to the Jews the result of their prejudice and unbelief. Already they had entered upon a path which they would steadily pursue until He should be led as a lamb to the slaughter. DA 164.4"
"From that time forth began Jesus to shew unto his disciples, how that he must go unto Jerusalem, and suffer many things of the elders and chief priests and scribes, and be killed, and be raised again the third day."
Both passages discuss Jesus's awareness of his impending suffering and death. The EGW passage expands on the reasons why Jesus didn't fully explain it to his disciples at that time, while Matthew 16:21 is the initial revelation of his suffering. The EGW passage amplifies the context and implications of the verse.