I can understand and as a conservative respect your desire for Old Testament proof. However, our Great Teacher, was not exactly what anyone would call conservative or conventional during His time on earth in a human body. Jesus came (in part) to show the world that spirit and flesh could come together completely in only One Person, the Son of God, born of Him.
Nicodemus may have been among other things considered to be a physician. I have dealt with many physicians. After studying and searching through all the parts of the human body, with hands, eyes and hearing what it is and is not, that becomes all that is real. I body, for the first few minutes after death, does not always look that different. What is missing? We believe as believers in Christ, that the real person, in spirit form or soul, is gone. Why, because the body does not work anymore.
Jesus could have also been preparing Nicodemus for the experience of His death. As a Pharisee, Nicodemus believe in the afterlife. It is not spelled out clearly in the The Old Testament. We do not understand it after the death of Jesus, except by faith in the unseen. Have we had anyone come back after being dead three days, other than Jesus, to say what is out there. Have we sent a probe to heaven to bring us back information of what it is really like?
This Jewish, very traditional, very steeped in the Old Testament literature, likely still would not accept very openly that resurrection from the dead was possible.
I believe, Jesus was simply trying to get Nicodemus to understand that having eyes he was not seeing and ears he was not hearing; the real issue. This is why Jesus chided him. With all that Nicodemus knew he could not understand spiritual concepts. He wants wanting to touch, see, smell or taste that Jesus was the Son of God. Jesus was amazed that Nicodemus had not learned that physical and spiritual can meet and in Christ they can grow together, but they are like two different planets in the universe, or stars. They can be identified as existing, but not touched and smelled and felt. They in the same universe but not on the same orbit. When we try to combine them with human tools they bombard one another.
Nicodemus should have been after all these years learned the "Typology" of The Temple and the sacrifices. He may have had some idea that they represented something other than just what was seen with the eyes. A man working in a slaughter house my have wiped gallons of blood from his apron and boots, but never related it to the fact that One born of God and Spirit could bleed. We who are supposed to be spiritual ought to know such and relate to it somehow, but we have to take it by faith the Blood of Jesus cleanses our sins.
I can relate to people who do not see anything spiritual to breaking and eating pieces of bread and sipping wine. It is one thing spiritually and another physically. I have filled the cups and broken crackers many times to be passed out in Memory of Jesus on the Cross.
Nicodemus by all rights, should have known Who Jesus was and the way He would bring salvation to all mankind, but he did not. Thousands of Jews in Jesus time on earth accepted Him as Son of God and the Lamb of God Who takes away the sins of the world.
Thousands of the hierarchy of Jewish tradition and practice, never understood. We cannot understand why they could not understand that Jesus was and is The Promised One. Guess what, we could be just like Nicodemus. We may practice Christian religion but do not identify personally with the fact that Jesus Christ is now spiritual and delivered to our hearts by the Spirit of God, not physically. We do not take Jesus bodily and say, come on and go the cross for me. The Jewish tradition and thinking could never picture a Messiah on a cross. Nicodemus, needed to struggle about which he was going to believe. The Old Testament way was with physical evidences of salvation like blood from bulls and burnt offerings, ritual, explicit rites by explicitly dissecting every law of the Old Testament and following it perfectly. Nicodemus did know the Old Testament, but he did not understand faith in the Unseen God to the point of putting it all together as it pointed our Jesus as being Christos. That is a spiritual thing. If it was not so, all of the Jews would have followed Jesus. The wiser we think we are the more we depend on ourselves for our answers. The more we walk by faith in the Unknown God and the Unseen Spirit, the more we admit our lack of knowledge no matter how educated we become.
I too, believe in scripture and verse as my only proof for a biblical argument or verification. However, if Jesus had picked such a thing, Nicodemus would have gone away justified or spent all night with Him with a good round of Jewish bickering. Nicodemus could stand his ground with any one wanting Old Testament proofs. Jesus gave that to some. He gave Nicodemus and God-modeled question that would lead him to not just "searching scripture" like you are doing. I believe Nicodemus went home and started researching as you have for Old Testament proofs. Having something proven physically and materially does not increase faith, as some suppose, but it aims faith in a different direction. Faith in its truest form is aimed at an unseen target. It is not just closing the eyes and shooting into the darkness. It is shooting into the unproven and still knowing that God is really there. It is taking our bow and arrows and not aiming at a seen target, but one much greater than physical goals and targets, it is aimed at Spirit and Water that is not seen but we get a taste of from time to time like a newborn baby, so that whether or eyes are focused or not we still reach because with know that milk is there. We know God is real, because we are born again into a life that is not just flesh and blood. We are born into a world where milk is not squeezed from the tits of a few verses, but comes directly by faith in The Word of God, Jesus Christ and His ways of Revealing Himself through Spirit and the water of tears or our prayers sitting in darkness and waiting for Him that we know is there when all proof has disappeared.
I apologize if I get a bit inspired. I am a retired chaplain and have been by many death beds, including that of my dear wife. Death and dying separates the "would be's" from the real believers. Facing death means facing the darkness and the nothing physical while the last part of physical fades away and still seeing the Light. I know He is there. If I forgot every verse of scripture that I have memorized over fifty years, I would still Know He was there. I am not special. I am a realist and part skeptic. But the unshakable parts of our Christian faith are there when nothing visible or physical else is left.