After that, he reincarnated into Hezekiah/Chizkiyahu King of Judah, to hint to what is written by our Sages, "In the days of the flood, G‑d hung it on Cain weakly, and with respect to him it says, "All that existed was eradicated." (Gen. 7:23, Breishit Raba 22:12) After it was rectified he was called ‘Chizkiah’, because through him Cain was nitchazaick [strengthened] from his weakness.

The generation of the flood was an expression in our history below of the mechanics of the world of Tohu above. Therefore did they do Tohu oriented sins.1 The general theme of the Tohu motion associates with Cain.2 He planted the root of its expression in the world. The principle Tohu theme of the vessels shattering left them weak. Chizkiyah, who fixed the Tohu/Cain root repaired and strengthened it.

...Hezekiah merited one-third of the portion of the firstborn that was meant for Cain...

The letters YHV from ELYHV/Eliyahu/Elijah were rectified. As a result, ChZKYHV/Chizkiyahu/Hezekiah merited one-third of the portion of the firstborn that was meant for Cain, who was the firstborn of Adam. They are: Priesthood, Kingship, and the Firstborn Right, mentioned by the Targum Yonatan on the verse, "Reuven, you are my firstborn." (Gen. 49:3)

Keter is the highest of the sefirot. It means crown - the king’s primary expression of royalty. It itself divides into three sub-coronets, (Zohar III Naso, Idra Raba) expressed in the world as the crowns of Firstborn, Priesthood, and Kingship.3 The perfect level is when they are all found together in one person.

The three heads are the ultimate source of the right/left/middle principle that governs existence. (Zohar III Naso, Idra Raba) The greatest manifestation of the absolute Divine unity is when they are all found in one individual.

Cain made great offences. He tended to do this only because he had super potential for good. He was supposed to embody all of the three heads of keter together. In place of this, he committed three major crimes.4 This ‘unraveled the bundle’, disallowing the three to express together - darkening the manifestation of keter.

Jacob attained a great degree of perfection. (Zohar, Ta’anit) Through this, his children stood in the heights of the universe. Reuben the firstborn was equipped to don Priesthood and Kingship. This would have made the tribes into a miniature Mashiach tikun and caused the final redemption to come much sooner; the Egyptian redemption would have been for all time. Still, the world was not yet ready for it. This caused a tremor in the family bond that pushed Reuben to disturb the bed arrangement of his father.5 (Gen. 35:23) The Shechinah/malchut rests on the beds of tzadikim. (Zohar) Malchut is the last sefira that ricochets up and binds with the first sefira - keter.6 "And he [Achashvairosh] placed a keter malchut [royal crown] on her [Esther’s] head - and he made her queen in place of Vashti." (Esther 2:17) It is specifically through malchut connection below that keter is completed and its three heads are bound together and come into expression. Upsetting the malchut connection again separated the three heads. As a result Reuben lost all three, and they were divided.7

The letters YHV give into the final H/malchut. They are rooted in the three heads. By fixing them, Chizkiyah, who is from Judah, was able to draw them to malchut and take his portion of the three heads - kingship.

Thus Hezekiah wore the crown of Kingship, and this is the secret of what our Sages say, "G‑d wanted to make Hezekiah the Mashiach8... (Sanhedrin 94a) The reason was because he was from Cain the firstborn, and so was he fitting to take the crown of Kingship and to be the future Mashiach. However, it didn’t happen because he didn’t say shirah [song].

...the final redemption comes through the song of the world-to-come...

Hezekiah was very righteous. He brought his generation to such a great level that even children were great Torah experts. (Ibid.) "Torah comes out from supernal chochmah." Mashiach’s job is to infuse the world with the step above - keter. This is reached through song. (Ki Ata Neri IV, by Rabbi Dovber of Lubavitch) Therefore, the final redemption comes through the song of the world-to-come (Tikunei Zohar, Likutei Moharan II 8) which Mashiach will sing and teach the world. Any messianic candidate can only be in the ball park of reaching this level by first attaining a great plateau of chochmah. Hezekiah did ascend to this place. All he had to do was sing to activate his messianic potential. The Rabbis do not explain why he did not do this.

" I’d like to teach the world to sing, in perfect harmony... "

[Translation and commentary by Perets Auerbach.]