What Reichu writes further up about the destrudo release makes great sense to me, but with a few additions/notes:
Rei clones have no souls, and therefore perhaps no AT-field. They would perhaps fall apart without a soul. Rei who has a soul, but is not created or born normally like a human, would maybe have some overlapping tendencies.
Destrudo is also mentioned once more in EoE, where Shinji's AT-field is in the process of breaking down.
In summary I think Rei and her clones have a predisposition against falling apart, but this isn't really related to the psyche. The psyche might be affected by this of course, so the other way around might apply.
This would also mean that we are talking about some energy field and not a chemical.
Archont wrote:An Rei saw that it was good.
Back on topic: I don't think Rei had a death wish.
Like you, I don't think Rei had a death wish either, but she did yearn to return to a state of nothingness, or just non-human form - not death, but to return to her true self, Lilith. Could be strands of the fractured souls pulling at eachother, I have no idea.
Still, Rei ends up dead more than once, but I believe her willingness to accept that has a very simple reason: She can be replaced, and she knows it. Now, not replaced entirely, but revived into a new body. So the things that make Rei Rei, her body and how people perceive her, can be replaced. She's got this figured out.
Rei is a rational and logical being (more than average), and she knows that if she can be reborn, and she already knows it has happened once, she'll try using that to her end. Meaning she can go further than any other pilot in risking herself, which explains her willingness to accept dangerous assignments.
This still doesn't change how she's unhappy and lonely. Being unique in a large underground facility, being treated as a tool, and knowing what Rei knows will make you unhappy.