If you were to stare evil in the eye, what would you see? What would be its character traits?
Of the many malevolent characters recorded in the Bible, Amalek, the grandson of Esau, stands out as the greatest villain. He is the archetypal enemy of our people. He is the father of the nation that first waged war against the Jewish people upon their miraculous emergence from their Egyptian bondage.
Throughout our long history, Amalek's murderous intentions have had many anti-Semitic heirs. One of these was Haman, in the Purim miracle, who sought to annihilate every Jew from the face of civilized society. Traditionally, any mortal threat to the Jewish people is referred to as an Amalekite design.
What are the origins of such a character, who has proven to be the nemesis of the Jewish people and their G‑dly quest throughout all time?
In Genesis 36:12, we are introduced to Amalek's parents. "Timna was a concubine to Elifaz, son of Esau, and she bore Amalek to Elifaz."
Some verses later, we are told more about Timna's background. "And the children of Lotan were Hori and Hemam and Lotan's sister was Timna."1
We are also given information about the status of Lotan, Timna's brother. "These are the chiefs who came of the Horites: the chief Lotan, the chief Shobal, the child Ziboen, etc."2
Elifaz's concubine, Timna, was no common woman, but was the product of a royal family, her brother claiming the position of one of the Horite chiefs.
The Talmud (Sanhedrin 99b) fills in some missing details by explaining that Timna sought to convert to Judaism and came to Abraham, Isaac, and Jacob but they refused to accept her. The Talmud asks why Timna gave birth to Amalek and concludes that it was because they rejected her.
Timna became a concubine to Elifaz instead, insisting, "It is better to be a maidservant to this nation than to be a princess in any other nation."
Being from the seed of Abraham and Sara was considered extremely prestigious. Timna perceived the great respect and honor given to this clan, and she was willing to sacrifice her personal dignity in order to be attached to such a prominent and respected people, even if her connection would be a servile one.
I've always been puzzled by this story.
Timna's actions seem so righteous, so altruistic and pure. Why then would they result in a child who represents the antithesis of goodness and who is the very paradigm of evil?
Our patriarchs and matriarchs selflessly gave of themselves to reach out to humanity and teach the beauty of monotheism and G‑d's path of truth. They eagerly taught and accepted converts into their midst. Avraham was the ultimate seeker of converts; in fact, that was his stated goal. If our patriarchs rejected Timna, there must have been a strong reason for them to do so, perceiving that her motives were insincere.
Timna was not searching for G‑d, but rather for her personal aggrandizement. Her motives were not selfless, but rather all about herself.
Had Timna truly wanted to join a nation serving G‑d and following His ways, she would not have "settled" for joining the family of Esau, whose path was the antithesis of the Abrahamitic teachings. Timna desired, rather, to be part of a powerful but not necessarily G‑dly or spiritual people.
She was willing to temporarily sacrifice her personal status, but only for what she perceived as a greater, more fulfilling gratification. Her actions were not about G‑d, but entirely about herself. Our perceptive patriarchs realized this and therefore rejected her from joining the nation of G‑d.
In the era of Redemption, evil will be eradicated and all mankind will be perfected. Only one nation—Amalek—will not be a part of this vision.
"Their hand is on G‑d's throne, G‑d shall be at war with Amalek for all generations."3
Amalek represent an attitude that is beyond repair because it is the opposite of G‑dliness. It is entirely egocentric, even while dressed up as an act of devotion to G‑d. These are the seeds that can grow into the most extreme acts of evil fathomable.
Because the greatest distortion of goodness is an act of malevolence adorned in the religious garb of purity, an act of selfishness acted out in the noble name of G‑d.

Wow, what a great insight!
Hadn't thought of it like this, that Timna clearly sought honor and prestige without being remotely interested in connecting to Hashem or working on her character or other spiritual inner work.
We obviously made a mistake by not accepting her. There is a discussion in the Talmud about whether or not she initially wanted to marry into the family. The answer is that she did want to marry and was not accepted. She should have been allowed to convert anyway. We have been punished for a long time for this. The Midrash explains that the sar (spiritual image) of Amalek is Satan himself. HaShem did not allow the Bnai Yisrael to annihilate Amalek since no nation can be destroyed before its sar in Heaven has fallen first. He will perish only when sin is no longer to be found in K'lal Yisrael. Every time a Jew sins, they add strength to the sar of Amalek. It is only when the Bnai Yisrael will be free from sin that Amalek will be destroyed (Alshich). This from The Midrash Says Shemot B'shalach page 161. Shalom.
Furthermore:
~ A woman once came to Rabbi Eliezer to convert, and said to him: “Bring me
near.” He said to her, “List for me your deeds.” She said: “My youngest son is
born of my eldest son.” He admonished her. She went to Rabbi Joshua, and he
received her. His students said, “Rabbi Eliezer drove her away, and you draw
her near!” He said, “When she set her mind to convert, she was no longer of
this world, as it is said, All who come to it (to the faith) shall not return (to
sin; Prov. 2:19)." --- Midrash Kohelet Rabbah 1:25
~ Turn back, my daughters... (Ruth 1:12) Rabbi Shmuel bar Nachmani said in
the name of Rabbi Yudan the son of Rabbi Chanina: Three times it says, turn
back, corresponding to the three times one must rebuff one who seeks to
convert. But if he persists further, we receive him. But Rabbi Yitzchak said:
The stranger did not lodge in the street. (Job 31:32) Always push away
with the left hand, and draw near with the right. --- Midrash Ruth Rabbah
2:16
Finally, according to Book of Elijah, chapter 24, as pointed out by Rabbi Gefen elsewhere:
"[Amalek] asked [his father Eliphaz], 'Father, who will inherit This World and the World to Come?' 'The Children of Israel,' replied [Eliphaz]. 'Go out and dig wells for them and fix roads for them. If you do so, your share will be with the lowly among them and you will enter the World to Come.'"
Shalom Dersu,
I agree with your comments. The question is, did Amalek do this? It seems obvious that the original son of Eliphaz (Amalek) was only human and that he did eventually pass away. Therefore what the Sages are referring to is the spiritual aspect of evil that Amalek represents. This evil has not been erased at this time.
Thank You,
Rabbi Jay