Sorry, but there’s not much we can do with the word nincompoop.
It was coined sometime in the last half of the seventeenth century, though variously spelled nicompoop, nickumpoop, nincumpoop, but no source has been established.
Dr. Samuel Johnson, in his dictionary of 1755, believed it to have been a corruption of the Latin phrase, non compos, “without ability,” but the earliest forms of the word do not support that theory.
It looks to us as though someone had merely elaborated upon the older ninny of almost identical meaning.