When the month of Elul arrives, the Jewish High Holidays are soon to follow, but what is so Jewish about these High Holidays (ימים נוראים lit. Days of Awe)? Unlike the three pilgrimage holidays (שָׁלשׁ רְגָלִים ), Rosh Hashanah and Yom Kippur don’t celebrate the Exodus from Egypt or the giving of the Torah to the Jewish People. Their only commonality shared by all Jewish holidays is that they are an adaptation of earlier Pagan holidays. Unlike Passover, Shavuot and Sukkot which were originally agricultural and harvest holidays, Rosh Hashanah is a deeply political holiday and it’s adaptation was not so much a transition as it was a radical paradigm shift.
As we shall see, the most important holiday celebrated in both Ancient Egypt and Mesopotamia was the annual New Year rebirth, judgment and coronation of the King as god. So the best introduction to Judaism’s rendition of this king-making celebration is to understand Judaism’s love-hate (mostly hate) relationship with kingship.
When thou art come unto the land which the LORD thy God giveth thee, and shalt possess it, and shalt dwell therein; and shalt say: ‘I will set a king over me, like all the nations that are round about me’;
thou shalt in any wise set him king over thee, whom the LORD thy God shall choose; one from among thy brethren shalt thou set king over thee; thou mayest not put a foreigner over thee, who is not thy brother.
Only he shall not multiply horses to himself, nor cause the people to return to Egypt, to the end that he should multiply horses; forasmuch as the LORD hath said unto you: ‘Ye shall henceforth return no more that way.’
Neither shall he multiply wives to himself, that his heart turn not away; neither shall he greatly multiply to himself silver and gold.
And it shall be, when he sitteth upon the throne of his kingdom, that he shall write him a copy of this law in a book, out of that which is before the priests the Levites.
And it shall be with him, and he shall read therein all the days of his life; that he may learn to fear the LORD his God, to keep all the words of this law and these statutes, to do them;
that his heart be not lifted up above his brethren, and that he turn not aside from the commandment, to the right hand, or to the left; to the end that he may prolong his days in his kingdom, he and his children, in the midst of Israel. Deuteronomy 17: 14-20)
כִּי-תָבֹא אֶל-הָאָרֶץ, אֲשֶׁר ה’ אֱ-לֹהֶיךָ נֹתֵן לָךְ, וִירִשְׁתָּהּ, וְיָשַׁבְתָּה בָּהּ; וְאָמַרְתָּ, אָשִׂימָה עָלַי מֶלֶךְ, כְּכָל-הַגּוֹיִם, אֲשֶׁר סְבִיבֹתָי
שׂוֹם תָּשִׂים עָלֶיךָ מֶלֶךְ, אֲשֶׁר יִבְחַר ה’ אֱ-לֹהֶיךָ בּוֹ: מִקֶּרֶב אַחֶיךָ, תָּשִׂים עָלֶיךָ מֶלֶךְ–לֹא תוּכַל לָתֵת עָלֶיךָ אִישׁ נָכְרִי, אֲשֶׁר לֹא-אָחִיךָ הוּא
רַק, לֹא-יַרְבֶּה-לּוֹ סוּסִים, וְלֹא-יָשִׁיב אֶת-הָעָם מִצְרַיְמָה, לְמַעַן הַרְבּוֹת סוּס; וַ ה’, אָמַר לָכֶם, לֹא תֹסִפוּן לָשׁוּב בַּדֶּרֶךְ הַזֶּה, עוֹד
וְלֹא יַרְבֶּה-לּוֹ נָשִׁים, וְלֹא יָסוּר לְבָבוֹ; וְכֶסֶף וְזָהָב, לֹא יַרְבֶּה-לּוֹ מְאֹד
וְהָיָה כְשִׁבְתּוֹ, עַל כִּסֵּא מַמְלַכְתּוֹ–וְכָתַב לוֹ אֶת-מִשְׁנֵה הַתּוֹרָה הַזֹּאת, עַל-סֵפֶר, מִלִּפְנֵי, הַכֹּהֲנִים הַלְוִיִּם
וְהָיְתָה עִמּוֹ, וְקָרָא בוֹ כָּל-יְמֵי חַיָּיו–לְמַעַן יִלְמַד, לְיִרְאָה אֶת- ה’ אֱ-לֹהֶיךָ, לִשְׁמֹר אֶת-כָּל-דִּבְרֵי הַתּוֹרָה הַזֹּאת וְאֶת-הַחֻקִּים הָאֵלֶּה, לַעֲשֹׂתָם
לְבִלְתִּי רוּם-לְבָבוֹ מֵאֶחָיו, וּלְבִלְתִּי סוּר מִן-הַמִּצְוָה יָמִין וּשְׂמֹאול–לְמַעַן יַאֲרִיךְ יָמִים עַל-מַמְלַכְתּוֹ הוּא וּבָנָיו, בְּקֶרֶב יִשְׂרָאֵל
The institution of the monarchy was the ultimate divine concession to the shortcomings and shortsightedness of the chosen people. This same sentiment is presented in the Book of Samuel (Samuel I 8: 4-22)
Then all the elders of Israel gathered themselves together, and came to Samuel unto Ramah.
And they said unto him: ‘Behold, thou art old, and thy sons walk not in thy ways; now make us a king to judge us like all the nations.’
But the thing displeased Samuel, when they said: ‘Give us a king to judge us.’ And Samuel prayed unto the LORD.
And the LORD said unto Samuel: ‘Hearken unto the voice of the people in all that they say unto thee; for they have not rejected thee, but they have rejected Me, that I should not be king over them.
According to all the works which they have done since the day that I brought them up out of Egypt even unto this day, in that they have forsaken Me, and served other gods, so do they also unto thee.
Now therefore hearken unto their voice; howbeit thou shalt earnestly forewarn them, and shalt declare unto them the manner of the king that shall reign over them.’
And Samuel told all the words of the LORD unto the people that asked of him a king.
And he said: ‘This will be the manner of the king that shall reign over you: he will take your sons, and appoint them unto him, for his chariots, and to be his horsemen; and they shall run before his chariots.
And he will appoint them unto him for captains of thousands, and captains of fifties; and to plow his ground, and to reap his harvest, and to make his instruments of war, and the instruments of his chariots.
And he will take your daughters to be perfumers, and to be cooks, and to be bakers. …..
And ye shall cry out in that day because of your king whom ye shall have chosen you; and the LORD will not answer you in that day.’
But the people refused to hearken unto the voice of Samuel; and they said: ‘Nay; but there shall be a king over us;
We should keep in mind that the appointment of a human King and the appointment of a human Messiah are one and the same.. both are a major concession to the lack of vision and faith by God’s flock. Both a King and the Messiah are the anointed of God 
The monarchy was accepted, with legal restrictions and much of the prophetic tradition represents a check and balance on the monarchy 
Getting back the New Year’s Coronation Festival in the Ancient Near East, the Classical study was written by Henri Frankfort and called Kingship and the Gods: A Study of Ancient Near Eastern Religion as the Integration of Society and Nature and is available for download here.
Frankfort details how in Mesopotamia the festival of the new year lasted twelve days; it was a time of purification, of renewal of the vegetation. It was also a time of dramatic reenactments, the most important of which were the rites of the Sacred Marriage, and the recitation of the Sumerian creation epic, Enuma elish. It was at this time that the destinies of both gods and mankind were fixed, and the king began his reign on new year’s day. (see)
One fascinating aspect of the Akitu involved a kind of ritual humiliation endured by the Babylonian king. This peculiar tradition saw the king brought before a statue of the god Marduk, stripped of his royal regalia and forced to swear that he had led the city with honor. A high priest would then slap the monarch and drag him by his ears in the hope of making him cry. If royal tears were shed, it was seen as a sign that Marduk was satisfied and had symbolically extended the king’s rule. Some historians have since argued that these political elements suggest the Akitu was used by the monarchy as a tool for reaffirming the king’s divine power over his people. (see)
Likewise in Ancient Egypt there was the Sed Festival held in the Fall hat celebrated the continued rule of a pharaoh. The ancient festival might, perhaps, have been instituted to replace a ritual of murdering a pharaoh who was unable to continue to rule effectively because of age or condition. … They primarily were held to rejuvenate the pharaoh’s strength and stamina while still sitting on the throne, celebrating the continued success of the pharaoh. The Sed-festival developed into a royal jubilee intended to reinforce the pharaoh’s divine powers and religious leadership.
Writes Frankfort: “
The Egyptian calendar started with the first day of the first month of the Season of Inundation (1 Thoth), a day originally coinciding with the beginning of the rise of the Nile. But four months later there was another new beginning: the inundation ended the Nile returned to its bed, and the new crops were sown. The first day of the first month of the “Season of Coming Forth” (1 Tybi) was consequently celebrated as a rite de passage appropriate to a new beginning, although it was not the Calendrical New Year’s Day. This “New Year’s Day” in autumn was presided over by a snake-demon called Nehebkau, a name which can be translated as “Bestower of Dignitaries” or as “Uniter of the Ka’s” (of Horus and Osiris), and we have , in both cases, an illusion to the definitive assumption of power by the new king. … it was fitting that a king should be crowned to re-establish harmony between nature and society which had been shattered by the death of the previous ruler. Hence it is said of Tuthmosis I, when he indicates the date for the coronation of Hatshepsut: “He knew that a coronation on New Year’s Day was good as the beginning of peaceful years.” (pp 103-4). 
This understanding of the context of the New Year’s Festival in the Ancient Near East, radically changes our understanding to the Jewish New Year holiday, Rosh Hashanah. What Rosh Hashanah becomes is a radical statement of independence of all human rule.
On Rosh Hashanah we declare God King as a direct and vocal rejection of the widespread and widely known (at the time) traditions of making a human of blood and flesh… into a divine king.
Although God as king always enters into our prayers (e.g. Blessed are You King of the Universe…), it is on Rosh HaShanah that we have the focal point on Malchiot – Kingship, culminating at the end of the Neilah service where we end the service with the threefold repetition of “Praised is His name, whose glorious kingdom for ever and ever,” that recalls the threefold declaration: “The Lord is king (present), the Lord was king (past), and the Lord will be king (future).”
Ultimately, it is in our New Year’s Festival that we reject our people’s request for a human king (and a human anointed one) as we reject the rule of any human being and we declare God is King. For a humanist… it doesn’t get any better, because the emphasis is not that God is King… but that no human can rule us. We say to all tyrants and others attempting to form our opinions and curtail our actions and imagination… you are not my boss.
To-morrow about this time I will send thee a man out of the land of Benjamin, and thou shalt anoint him to be prince over My people Israel, and he shall save My people out of the hand of the Philistines; for I have looked upon My people, because their cry is come unto Me.’ (Samuel I 9: 16)
כָּעֵת מָחָר אֶשְׁלַח אֵלֶיךָ אִישׁ מֵאֶרֶץ בִּנְיָמִן, וּמְשַׁחְתּוֹ לְנָגִיד עַל-עַמִּי יִשְׂרָאֵל, וְהוֹשִׁיעַ אֶת-עַמִּי, מִיַּד פְּלִשְׁתִּים: כִּי רָאִיתִי אֶת-עַמִּי, כִּי בָּאָה צַעֲקָתוֹ אֵלָי
And the spirit of the LORD will come mightily upon thee, and thou shalt prophesy with them, and shalt be turned into another man. Samuel I 10:6
וְצָלְחָה עָלֶיךָ רוּחַ ה’, וְהִתְנַבִּיתָ עִמָּם; וְנֶהְפַּכְתָּ, לְאִישׁ אַחֵר
As Frankfort, Wilson, and Jakobsen write in The Intellectual Adventure of Ancient Man: An Essay of Speculative Thought in the Ancient Near East (p348) “A jealous concern for their traditional prerogatives was kept alive among the people by various agitators, notably the prophets. Nathan’s rebuke of David, as Elijah’s of Ahab, was a direct denial of the assumptions of divine right and a bold affirmation of the principle that the king was amenable to the same standards of right, the same pervasive natural law as his humblest subject. Here, too, it is apparent, was the principle basic to the entire attitude of the prophets and other progressive thinkers toward the monarchy: the king ruled, not by divine right, but under divinely imposed responsibility”
For further reading regarding Nisan and Tishrei as Kinmaking New Year’s festivals including actual Mesopotamian liturgy that has striking parallels to the Rosh Hashanah liturgy see Kingship and the Gods chapter 22 The New Year’s Festival pp 313-) here