Thank you my dear friend for this very excellent question.  No, I wouldn’t say that the Israelites believed in reincarnation; however, there are a series of Old Testament prophesies about the raising up of a prophet before the coming of the Messiah that the people of Israel were looking forward to. But now, what do these verses in Matthew 16 say after the Lord Jesus asked His disciples who the people believed He was? “And they said, Some say that Thou art John the Baptist: some, Elias; and others, Jeremias, or one of the prophets. He saith unto them, But whom say ye that I am? And Simon Peter answered and said, Thou art the Christ, the Son of the living God,” (Matthew 16:14-16).

Now, I will admit that Herod, when he heard about Christ had a fear that John the Baptist may have risen from the dead. We read about this fear in Mark 6:16 which says, “But when Herod heard thereof, he said, It is John, whom I beheaded: he is risen from the dead.” But, this was, I think, mostly superstition on Herod’s part due to his own sin in having John killed for telling the truth about Herod’s immoral and illegal relationship with his brother Philip’s wife. So, Christ Jesus was clearly not a resurrected John the Baptist, a point that is affirmed by Scripture (John 1:8). But now, as I have mentioned, the Old Testament prophesies do in fact point to the raising up of a special prophet or a messenger in the character of Moses and Elijah, who was to “prepare” the way of the Lord (Deuteronomy 18:15; Isaiah 40:3; Malachi 3:1; John 1:6-8). Thus, these prophesies do not refer to Christ Himself, but to a forerunner of Christ.

But now, who was John if he was not the Christ? The Jews were certainly and rightly waiting for Elijah or another prophet to arise before the Messiah should come. And, considering the question as to John the Baptist being the prophet spoken of in Matthew 16, The Lord Jesus made this connection Himself in Matthew 11:13-14: “For all the prophets and the law prophesied until John. And if ye will receive it, this is Elias, which was for to come.” And yet, you might also notice that John denies being Elijah or that other prophet in John 1:21-23, and this can be a bit confusing. So, I will quote from MacDonald’s commentary on John 1:21-23 in order to clarify what John was saying as follows: “The Jews expected Elijah to return to the earth prior to the coming of Christ (Malachi. 4:5). So, they reasoned that if John was not the Messiah, then perhaps he was Elijah. But John assured them that he was neither the Messiah nor even one of the great OT prophets. In Deuteronomy 18:15, Moses had said, “The Lord your God will raise up for you a Prophet like me from your midst, from your brethren. Him you shall hear.” The Jews remembered this prediction and thought that John might be the Prophet mentioned by Moses. But again, John said that it was not so.  In John 1:23 he said, “I am ‘The voice of one crying in the wilderness.’” In answer to their query, the Baptist quoted from Isaiah 40:3, where it was prophesied that a forerunner would appear to announce the coming of Christ. In other words, John stated that he was the forerunner who was predicted. He was the voice, and Israel was the wilderness. Because of their sin and departure from God, the people had become dry and barren, like a desert. John spoke of himself simply as a voice. He did not pose as a great man to be praised and admired….” So, John denied that he was the prophet to come, though in fact his appearing certainly prefaced the first advent of our Lord Jesus. But, since he was not believed by very many, it does remain for the primary application of these prophesies to be fulfilled when Christ returns to the earth in glory and power in the end times, just before that great and terrible day of the Lord (which is the Great Tribulation-see Zechariah 14: 1-5; see also Malachi 4: 5, 6; Matthew 11: 14; Luke 1: 17).

To summarize, John the Baptist did indeed come in the spirit of Elijah to make straight the way of the Lord. however, Israel did not receive their King, so later as the Great tribulation approaches, there will be another who comes in the spirit of Elijah, or perhaps the resurrected Elijah himself, who will precede this second coming of Christ, which we see clearly in the words of Malachi 4:5: “Behold, I will send you Elijah the prophet before the coming of the great and dreadful day of the LORD….”  (SF)  (562.3)