I see you gave your definition of death and said it was from the bible, but I don't see anywhere that you showed where it was from in the bible. The second death is easy. It's defined in Rev 20 as "the lake of fire", which is NOT the same as defining it as "separation", though that may indeed be part of it.
If the second death is defined as something besides separation, and the bible never explicitly defines the first death as separation, are you sure you aren't being too hasty in defining death as separation and calling it the biblical definition?
I had assumed that you were familiar with the Bible, so I gave you an overview of the things I shared. My mistake. However, I'm not going to post every verse that corresponds to what I'm about to say. You can either review the Bible on your own, or ask someone to show you know who cares about your blatant ignorance.
The Bible does explicitly tell us that Adam died the day he ate from the tree, yet Adam still lived.
We also know, or should know, if we've read the Bible, that because of his death from his disobedience, death spread to all men, for the wages of sin is death. So, what died when Adam sinned, since he still lived and all those after him still lived, even though the Bible says they are already dead.
"And you He made alive
, who
were dead in trespasses and sins"
Whether you agree or not, or whether you are satisfied with my answers or not, the Bible is clear that ALL men are dead because of the sin of one man, and because all men are dead all men are sinners.
"Wherefore, as by one man sin entered into the world, and death by sin; and so death passed upon all men, for that all have sinned"
So, what does it mean when the Bible says that Adam died, if he was still living? And what does it mean if all men are dead, even though they are living. Well, we know that it is the Spirit that gives life (Jn 6:6; 2 Cor 3:6), and anyone who is dead because of sin, receives His life when they are indwelt by His Spirit, having believed the gospel.
"Hereby know we that we dwell in him, and he in us, because he hath given us of his Spirit." 1 Jn 4:13
We were once in Adam (dead), but are now in Christ (alive)
"For as in Adam all die, so also in Christ all will be made alive." 1 Cor 15:22
"And this is the record, that God hath given to us eternal life, and this life is in his Son. He that hath the Son hath life; and he that hath not the Son of God hath not life." 1 John 5:11-12
So, we know that men are dead before they receive life. Men are separate from life, because they are dead. The Bible defines death as being separate from having life. The Bible also describes all those who receive the life of God as having died, and yet they live.
"I am crucified with Christ: nevertheless I live; yet not I, but Christ liveth in me: and the life which I now live in the flesh I live by the faith of the Son of God, who loved me, and gave himself for me" Gal 2:20
"For you
have died and your
life is hidden with Christ in God" Colossians 3:3
"Now if we have
died with Christ, we believe that we shall also live with Him"
Having been crucified with Christ and having died with Christ, is to be separated from who we were in Adam, and also to be separated from sin, and the Law.
"But now we have been released from the Law,
having died to that by which we were bound, so that we serve in newness of the Spirit and not in oldness of the letter."
"How shall we, that are
dead to sin, live any longer therein?"
"Wherefore if
ye be dead with Christ from the rudiments of the world, why, as though living in the world, are ye subject to ordinances"
These are just a few example, and there are many, many more where the Bible defines death as having become separated from who, what, where you once were to who/what/where you are now, having passed from death to life.
Jesus died on the cross and yet only His body lied in the tomb. Jesus was still active before He raised His body (temple).
"For Christ also suffered for sins once for all
time, the just for
the unjust, so that He might bring us to God, having been put to death in the flesh, but made alive in the spirit; in which He also went and made proclamation to the spirits in prison"
The apostle Paul also defined death as being separated from the body and yet alive with God.
"We are confident, I say, and willing rather to be absent from the body, and to be present with the Lord."
I could go on and on and on, but I'm a bit apathetic about providing for you what is so obvious throughout the entirety of the Bible.