I do not believe the Ring of Gyges preceded Plato making it up for The Republic... Where are you getting 4000 years?
Also maybe not seeing the message or connection here... That myth isn't really about who has power or not, right? It's kind of just a trite little "why you should do good even when no one is watching" thing. It just serves Socrates for his argument with Thrasymachus, and leads us into book 2 where it really gets going with Glaucon and all that. This is from memory so I might be a little off.
I got it from Tamar Gendlers philosophy and human nature course on open yale courses. She says it was a popular folk story passed down orally much before it was written in a book. Plato used it because people grew up hearing the story.
The story is asking whats the source of morality? Who decides where the lines are? And its not scientists. Science produces the Ring.
I was wrong, it's in Book II. This is "Socratic irony", its Glaucon speaking, assuming the position of an argument from earlier. Socrates himself of course doesn't believe in this conclusion... we are going to learn later that justice is a form, based on the Good! This is all the doxa of one still in the cave.
> According to the tradition, Gyges was a shepherd in the service of the king of Lydia; there was a great storm, and an earthquake made an opening in the earth at the place where he was feeding his flock. Amazed at the sight, he descended into the opening, where, among other marvels, he beheld a hollow brazen horse, having doors, at which he stooping and looking in saw a dead body of stature, as appeared to him, more than human, and having nothing on but a gold ring; this he took from the finger of the dead and reascended. Now the shepherds met together, according to custom, that they might send their monthly report about the flocks to the king; into their assembly he came having the ring on his finger, and as he was sitting among them he chanced to turn the collet of the ring inside his hand, when instantly he became invisible to the rest of the company and they began to speak of him as if he were no longer present. He was astonished at this, and again touching the ring he turned the collet outwards and reappeared; he made several trials of the ring, and always with the same result—when he turned the collet inwards he became invisible, when outwards he reappeared. Whereupon he contrived to be chosen one of the messengers who were sent to the court; whereas soon as he arrived he seduced the queen, and with her help conspired against the king and slew him, and took the kingdom. Suppose now that there were two such magic rings, and the just put on one of them and the unjust the other; no man can be imagined to be of such an iron nature that he would stand fast in justice. No man would keep his hands off what was not his own when he could safely take what he liked out of the market, or go into houses and lie with any one at his pleasure, or kill or release from prison whom he would, and in all respects be like a God among men. Then the actions of the just would be as the actions of the unjust; they would both come at last to the same point. And this we may truly affirm to be a great proof that a man is just, not willingly or because he thinks that justice is any good to him individually, but of necessity, for wherever any one thinks that he can safely be unjust, there he is unjust.
https://gutenberg.org/cache/epub/1497/pg1497.txt