Targum Pseudo-Jonathan on Genesis 9:16 sharpens the promise one more time. The bow shall be in the cloud, and I will look upon it, to remember the everlasting covenant between the Word of the Lord and every living soul of all flesh that is upon the earth.
Two details shine. First, God Himself looks at the rainbow. It is not only a sign for us. It is a sign for the Holy One. That is why the sages were careful about gazing at rainbows — they taught that staring at the bow is a kind of intrusion on heaven's private moment of memory.
Second, the Aramaic calls it an everlasting covenant, keyam alma, a covenant without expiration. The word olam in Hebrew means both "world" and "forever." In the Targum's language, the promise is stretched to the very edges of time.
Jewish tradition teaches that the reason we do not gaze too long at the rainbow is because it represents our generation's own frailty — that humanity does not always deserve even this minimal assurance, and heaven is being merciful to offer it. The very bow is an admission that we are fragile, and a promise that fragility will not be punished with another Flood.
The takeaway the Maggid draws: never take the rainbow for granted. Every time you see one, you are standing inside a promise older than every nation and every calendar.