The Bible calls this final separation from God “the second death.”
The Bible doesn’t define death as separation from God. Rather sun separates someone from God in the sense He won’t hear them nor pay attention to them, but it isn’t permanent. God will come close again if they repent.
Isaiah 59:1,2
1Behold, the LORD'S hand is not shortened, that it cannot save; neither his ear heavy, that it cannot hear:
2But your iniquities have separated between you and your God, and your sins have hid his face from you, that he will not hear.
In the Book of Revelation the lake of fire is so described (Revelation 20:14). Jesus also identified Gehenna as a second death when He warned: “Do not be afraid of those who kill the body but cannot kill the soul. Rather, be afraid of the One who can destroy both soul and body in hell [Gehenna]” (Matthew 10:28; see also Luke 12:4,5). This clearly refers to another death after the physical death of the body.
agreed. This is post-resurrection destruction of the soul and body via the lake of fire.
It is also clear that this death is different in order and in kind. As physical death is separation from the body and from the environment of this life, so the second death is a final and eternal separation from God and from the life to be enjoyed in the new creation.
I honestly think you’re defining death incorrectly since death isn’t a separation from God. Death is actually just death. Sin is temporary separation from God. Were Adam and Eve eternally separated from God they day they died spiritually? Was David separated from God forever when he sinned? No, God still helped them.
Among those consigned to this second death will be all who take the mark of the beast (Revelation 14:9–11). These will be tormented with fire and brimstone in the presence of the angels and Christ. That is, though shut off from the new creation in the lake of fire, they will be able to see the Lamb of God they rejected
That passage doesn’t say the torment is eternal.
just as Lazarus was able to see across the great gulf between Hades and Abraham’s bosom (Luke 16:23).
The story of the rich man and Lazarus is a parable and it doesn’t say the torment lasts forever.
Again, they will not be annihilated, for “the smoke of their torment rises for ever and ever. There is no rest day or night” (Revelation 14:11). They will be forever denied the rest promised to the saints.
They are not immortal for only those saved by Christ can be immortal.
It says the smoke rises forever. In Isaiah 34:10 Edom, a place on Earth, is said to be burning forever and that it has smoke rising forever, but it’s not still burning and smoking. This is called apocalyptic language and it’s meant to be dramatic, not literal in this case.
“No rest day or night” does not presuppose eternity. Literally that means for one day and one night they won’t rest. There is pain involved in the second death, but it isn’t eternal.
None of these passages indicates any promise of rehabilitation or restoration once the final judgment is pronounced. No sanctifying agent is revealed in connection with the lake of fire or Gehenna. The fire is parallel to the “worm” of Mark 9:44,46,48 (KJV). It is looked at as punitive, not purifying. There will be no second chance. This should stir the Church to proclaim the message, “Now is the day of salvation” (2 Corinthians 6:2).
I am not saying there is a second chance post-judgement is the wicked. They’ll be put to death, destroyed soul and body, just like the Bible says. They won’t be conscious living forever in torment.