It’s the sort of evidence you would expect to see when two sources are based on eyewitness accounts. One account of an event omits a piece of information which is filled in by another account in a seemingly unintentional fashion.
An Example of an Undesigned Coincidence
Sarah says she saw Bob walking to the shopping center in a suit on a Saturday morning. Taylor, who works in the shopping center, tells you she interviewed Bob for a sales job on Saturday morning.
The distinct details each witness gives subtly help explain why Bob was wearing a suit and why he went to the shopping center. The more instances of these coincidences we have, the less likely intentional fabrication becomes.
Here are several examples of undesigned coincidences in the Bible:
MENDING NETS
James and John were mending their nets (Matt. 4:21) when Jesus called them to follow him. Luke explains Jesus’ miracle catch of fish was breaking their nets (Luke 5:6) before they left everything to follow Jesus (v. 10–11), yet Matthew does not mention this miraculous catch.
The Healing at Peter's House
Mark 1:21 and 29-32 clarifies why they waited until the evening: the event happened on the Sabbath, and the people would have waited until the Sabbath ended at sundown to bring their sick, as public healing was controversial on the Sabbath. Mark's casual mention of the Sabbath is not presented as an explanation for Matthew's timing, but it fits perfectly.
The Feeding of the 5,000
John 6:4 casually notes, in a different context within his narrative, that the miracle occurred around the time of the Passover festival. Passover happens in the spring (March/April), the only time of year when the grass in that region would be green after the winter rains.
John 6:5 records Jesus asking Philip where they should buy bread. One might wonder why Philip was singled out.
Luke 9:10 (in the context of the same event) and John 1:44 (in an unrelated passage) provide the answer: the miracle took place near the town of Bethsaida, which was Philip's hometown. Jesus naturally turned to the disciple with local knowledge.
Luke 8:3 provides a potential explanation in an unrelated list of Jesus' female followers: one of them was Joanna, "the wife of Chuza, Herod's household manager". Joanna could have been an internal source of information from Herod's palace.
The Dispute Among the Disciples and the Foot-Washing
John 13:4-15 describes the seemingly spontaneous event of Jesus washing his disciples' feet during the meal. John doesn't mention the dispute, and Luke doesn't mention the foot-washing, but together, the foot-washing serves as a powerful, practical demonstration of the exact lesson Jesus was teaching in response to their argument in Luke.
Mary and Martha
In Luke 10:38-42, we get the famous story of Jesus visiting Mary and Martha of Bethany. Martha, the practical sister, is trying to get the house in tip-top shape for Jesus and becomes annoyed at her sister Mary, the emotional sister, who is just sitting at Jesus’ feet.
The Sons of Thunder
Mark 3:17 tells us that James and John, the sons of Zebedee, were nicknamed “the sons of thunder” by Jesus. Mark never explains why Jesus would give these two such a memorable sobriquet. However, Luke’s gospel tells the story of Jesus being rejected by the Samaritans because he is a Jew on his way to Jerusalem. Luke continues: “And when his disciples James and John saw it, they said, “Lord, do you want us to tell fire to come down from heaven and consume them?” But [Jesus] turned and rebuked them” (9:54-55).
The Transfiguration
Upon coming down from the mount of transfiguration, Luke’s gospel tells us that the disciples “kept silent and told no one in those days anything of what they had seen” (Luke 9:36). But why? Wouldn’t you tell somebody if the rabbi you were following starting glowing white and had a conversation with Moses and Elijah? Luke provides no answers.
Pilate's interrogation
In Luke 23:1-4, Pilate asks Jesus whether he is a king, and Jesus gives an answer that is certainly not a denial and that many scholars take for a terse, idiomatic acknowledgement. Then Pilate declares that he finds him innocent. How can this be explained? Answer: Luke is giving only a summary of the interview. In a fuller account, we discover that Jesus told Pilate that His kingdom was not of this world. (John 18:36)
Also, in John 18:32, Pilate asks Jesus whether he is a king. What prompted that question? (Nothing earlier in the chapter indicates that this was a charge leveled against Jesus.) Answer: Though John does not record it, the Jews did make that very charge against Jesus. (Luke 23:1-2)
An Accusation at the Cross
Mark records that people who saw Jesus on the cross derided him by saying, “Aha! You who would destroy the temple and rebuild it in three days, save yourself, and come down from the cross!” (Mark 15:29-30). Yet nowhere in Mark (or Matthew or Luke, for that matter) does Jesus make this claim. It seems to come out of nowhere.
It's highly unlikely that later fabricators from all different parts of the world, decades after Jesus, tie each other’s loose ends up so neatly in such a subtle fashion if the recorded narratives were completely disconnected from the historical events? It’s far more likely the Gospel authors were referring to eyewitness history, and not making up history.