>Sorry - misunderstood what you were asking... Yes, spiritual death is eternal separation from God. Just means there is no chance of returning someday. I don't think the Bible uses that term ("eternal death") so please excuse my feeble attempt to paraphrase what's in there...
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>Reincarnation is not a concept from the Bible. There is physical death and spiritual death.

's what I'm saying - if reincarnation was an idea circulating at the time, among others, that would mean that people were thinking of death as temporary. The new religion would then have to underline that in their terms there's no temporary death (unless you're the one exception they make) by adding the word "eternal" so to make things clear.

Doesn't really matter if it doesn't say so in those exact words - you got it from there this way or another, and I trust you were just trying to convey the meaning the best way. So while actual words used may differ, I think this is what it was for.