The idea that Luke couldn’t be an eyewitness of Jesus’ teaching and work comes from the fact that most Biblical scholars believe his Gospel was written later in the 1st century AD, perhaps in the 80s, but some would date it even later. Therefore, the premise of Luke being an eyewitness seems out of the question, and even the proposition that there existed eyewitnesses of Jesus ministry at these late dates seems improbable, unless they were quite young witnesses at the time; for example, a witness in his 20s during Jesus’ ministry would be at least in his 70s by the time of the most accepted date for writing Luke. What can we say of these things?
Many scholars point out that Luke’s preface (Luke 1:1-4) puts the eyewitnesses of Jesus’ ministry in the past. They conclude that Luke 1:2 implies the Apostles and their ministers (the eyewitnesses who delivered the Gospel to us) were dead at the time of Luke’s writing, pointing out that both Luke (v.3) and the “many” others (v.1) have at this late date taken in hand to set forth a narrative of the Gospel that was delivered to and believed by Luke and the “many” who remain. But, was Luke’s narrative written late? Notice:
“…it seemed fitting for me as well, having investigated everything carefully from the beginning, to write it out for you in consecutive order, most excellent Theophilus;” (Luke 1:3 NASB)
“…So it seemed good to me as well, because I have followed all things carefully from the beginning, to write an orderly account for you, most excellent Theophilus,” (Luke 1:3 NET.) [emphasis mine in both translations]
Did Luke carefully investigate (G3877), in the sense of conducting research, everything that Jesus said and did from the beginning, or did he carefully follow (G3877), in the sense of mentally keeping a close eye on, all things Jesus said and did from the beginning? There is belief among some scholars that parakoloutheo (G3877) does not mean to investigate. The same word is used in 2Timothy 3:10, but did Timothy investigate Paul’s doctrine and manner of life or did he mentally follow, even witness, Paul’s doctrine and manner of life?
Josephus uses this same word (G3877) in his work:
“…A strange sort of accusation and calumny this! since every one that undertakes to deliver the history of actions truly ought to know them accurately himself in the first place, as either having been concerned in them himself, or been informed of them by such as knew them.” [Josephus; Against Apion I; section 10; Winston Translation – emphasis mine]
Notice that “having been concerned (G3877) in them himself” is placed in contrast with “been informed of them by such as knew them.” Thus, we see that parakoloutheo (G3877) concerns not ‘research’ but mentally following and recording what one knew to be true by experience. In the above quotation Josephus was defending his own works: “The Jewish Wars” against the criticism of some men and claimed concerning the siege of Jerusalem:
“…there was nothing done which escaped my knowledge; for what happened in the Roman camp I saw, and wrote down carefully; and what informations (sic) the deserters brought [out of the city], I was the only man that understood them…” [Josephus; Against Apion I; section 9; Winston Translation]
What Luke, therefore, means in the preface to his Gospel (Luke 1:1-4) is that, while he had the eyewitness account of the Apostles available to him, he was also able to supplement what they were teaching through what he carefully followed and recorded in his own experience. He may not have been with Jesus from the beginning, but Luke would have been able to offer what he followed and recorded from the beginning of his association with Jesus’ ministry. What might Luke have offered Theophilus concerning his own experience with Jesus?
Much of what is peculiar to Luke is found in what many scholars refer to as ‘Jesus march toward Jerusalem,’ i.e. Luke 9:51 to Luke 18:17. It has been put forth by some that it is possible, even probable, that Luke was one of the 70 sent forth by Jesus. The mission of the 12 Apostles sent out two by two seems important enough to be reported by all three Synoptics. However, only Luke records the mission of the 70. Although Luke offers only 7 verses to describe the important mission of the Twelve, he gives us 24 verses to describe the less important mission of the 70! This is quite odd, unless Luke is offering his own eyewitness account which would have been very important to himself, and would show Theophilus Luke’s own qualifications to express the certainty of those things about which he had been informed (Luke 1:4).
While this point of view of Luke being one of the 70 cannot be proved without doubt, it certainly does fit the context of parakoloutheo (G3877) in Luke 1:3, and something like being a member of the 70 (Luke 10:1-24) should have occurred. Otherwise, how would Luke have “closely followed” the events of Jesus’ ministry, unless he lived in Judea or Galilee where those things took place? It would be necessary for him to be close enough to receive news of Jesus’ activity on a regular basis, and even participate in what Jesus was doing on occasion. If not, how could it be said that Luke “carefully” (G199) followed (G3877) everything Jesus said and did from the beginning?
 See John Wenham’s Identification of Luke, Evangelical Quarterly 63:1 (1991), 3 – 44, from which my argument here is based.