Could you, please, explain the meaning of "the bright eye" here?

And God is never far away.
Into the mercy seat I climb
My head is shaved, my head is wired
And like a moth that tries
To enter the bright eye
I go shuffling out of life
Just to hide in death awhile

Does it try to compare a moth's urge to enter the light to his desire to leave this world?
I think you're right. Is this about an execution?

He seems to suggest that both he and the moth look at "entering the bright light" as a better, but temporary condition. (mercy seat)

People with "near death experiences" frequently speak of the bright light.
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Thanks, Avangi.

Yes, it's about an inmate on death row. I guess the mercy seat refers to both the electric chair and the throne of God. (he literally climbs into the electric chair and upon his death his soul rises to the Heavens to face God).

You could be right about NDE. It makes sense.
I think it's an exceptionally effective poem.