Universal theory of Biblical eye-raising

Question

Do any of the commentaries or Midrashim offer a universal interpretation (perhaps of the form "any time you see this, it means that") of Biblical idiom of "raising eyes"?

Below are some examples that happened to come to hand. I'm sure there are many others, in many different contexts. Maybe it's just a simple idiom for looking, but I think I've heard somewhere that it can be taken to mean something more specific.

Examples:

• Gen. 13:10

  וַיִּשָּׂא לוֹט אֶת עֵינָיו וַיַּרְא אֶת כָּל כִּכַּר הַיַּרְדֵּן כִּי כֻלָּהּ מַשְׁקֶה לִפְנֵי שַׁחֵת יְ־הֹוָ־ה אֶת סְדֹם וְאֶת עֲמֹרָה כְּגַן יְ־הֹוָ־ה כְּאֶרֶץ מִצְרַיִם בֹּאֲכָה צֹעַר׃

  And Lot raised his eyes, and he saw the entire plain of the Jordan, that it was entirely watered; before the Lord destroyed Sodom and Gomorrah, like the garden of the Lord, like the land of Egypt, as you come to Zoar.

• Gen. 24:64

  וַתִּשָּׂא רִבְקָה אֶת עֵינֶיהָ וַתֵּרֶא אֶת יִצְחָק וַתִּפֹּל מֵעַל הַגָּמָל׃

  And Rebecca lifted her eyes, and saw Isaac, and she let herself down from the camel.

• Gen. 37:25

  וַיֵּשְׁבוּ לֶאֱכָל לֶחֶם וַיִּשְׂאוּ עֵינֵיהֶם וַיִּרְאוּ וְהִנֵּה אֹרְחַת יִשְׁמְעֵאלִים בָּאָה מִגִּלְעָד וּגְמַלֵּיהֶם נֹשְׂאִים נְכֹאת וּצְרִי וָלֹט הוֹלְכִים לְהוֹרִיד מִצְרָיְמָה׃

  And they sat down to eat a meal, and they lifted their eyes and saw, and behold, a caravan of Ishmaelites was coming from Gilead, and their camels were carrying spices, balm, and lotus, going to take [it] down to Egypt.

• Deut. 3:27

  עֲלֵה רֹאשׁ הַפִּסְגָּה וְשָׂא עֵינֶיךָ יָמָּה וְצָפֹנָה וְתֵימָנָה וּמִזְרָחָה וּרְאֵה בְעֵינֶיךָ כִּי לֹא תַעֲבֹר אֶת הַיַּרְדֵּן הַזֶּה׃

  Go up to the top of the hill and lift up your eyes westward and northward and southward and eastward and see with your eyes, for you shall not cross this Jordan.

• Deut. 4:19

  וּפֶן תִּשָּׂא עֵינֶיךָ הַשָּׁמַיְמָה וְרָאִיתָ אֶת הַשֶּׁמֶשׁ וְאֶת הַיָּרֵחַ וְאֶת הַכּוֹכָבִים כֹּל צְבָא הַשָּׁמַיִם וְנִדַּחְתָּ וְהִשְׁתַּחֲוִיתָ לָהֶם וַעֲבַדְתָּם אֲשֶׁר חָלַק יְ־הֹוָ־ה אֱלֹהֶיךָ אֹתָם לְכֹל הָעַמִּים תַּחַת כָּל הַשָּׁמָיִם׃

  And lest you lift up your eyes to heaven, and see the sun, and the moon, and the stars, all the host of heaven, which the Lord your God assigned to all peoples under the entire heaven, and be drawn away to prostrate yourselves before them and worship them.

Answer 1

Lifting

According to the Ksav Sofer, lifting the eyes is an "aha!" moment, the eyes meaning the intellectual eyes. Although he does not elaborate on each example, here are 2:

וַיִּשָּׂא לוֹט אֶת עֵינָיו וַיַּרְא אֶת כָּל כִּכַּר הַיַּרְדֵּן כִּי כֻלָּהּ מַשְׁקֶה לִפְנֵי שַׁחֵת יְ־הֹוָ־ה אֶת סְדֹם וְאֶת עֲמֹרָה כְּגַן יְ־הֹוָ־ה כְּאֶרֶץ מִצְרַיִם בֹּאֲכָה צֹעַר׃

And Lot raised his eyes, and he saw the entire plain of the Jordan, that it was entirely watered; before the Lord destroyed Sodom and Gomorrah, like the garden of the Lord, like the land of Egypt, as you come to Zoar.

'Lot believed in G-d and accepted the faith of Avraham because he saw Avraham's success in everything, but he saw, stared and understood that also the wicked dwell in peace and quiet and they have it good. Because of this, he started figuring that everything is by chance, not Divine supervision- success is not dependent on serving G-d and faith in him. Therefore, he traveled from the "kadmon" of the universe. Now the verses are explained well: Lot lifted his eyes- the eyes of his intellect, he saw, stared and understood and he saw the entire plain of the Jordan, that it was entirely watered...They were bad sinners, promiscuous, as Rashi wrote, like the land of Egypt- similar to Egypt who were famous for their promiscuity- such was the plain. In spite of this, Lot understood that these wicked people got rich though this. He said- why should I be loaded up with the yoke of Avraham's faith. So Lot chose the entire Jordan plain...'

וַיִּשָּׂא אַבְרָהָם אֶת-עֵינָיו, וַיַּרְא וְהִנֵּה-אַיִל, אַחַר, נֶאֱחַז בַּסְּבַךְ בְּקַרְנָיו; וַיֵּלֶךְ אַבְרָהָם וַיִּקַּח אֶת-הָאַיִל, וַיַּעֲלֵהוּ לְעֹלָה תַּחַת בְּנוֹ.

Avraham lifted his eyes and saw- behold! a ram, afterwards, caught in the entanglements by its horns. Then Avraham went, took the ram and offered it as an olah instead of his son.

'In the midrash Tanchuma: G-d said to Avraham- when your children sin, they will blow the shofar on the New Year and I will atone for them. Avraham said- What is [a] shofar? G-d said- Return behind you. Just then, Avraham lifted his eyes and saw...and he took the ram. It is necessary to ask- how didn't Avraham know what a shofar was? It is also necessary to ask- what is 'return behind you'? It appears to me, for [the sages] said- Shofar= Beautify (shifru) your actions. That is what G-d said to Avraham- when you blow the shofar before me...I forgive you, that means when they repent. But Avraham did not understand what the purpose of the shofar was- how through blowing the shofar will there be atonement for them? G-d said- return behind you, that is the idea of repentance and the shofar hints that one should return behind himself and return from the path he has walked in. Just then, Avraham lifted his eyes, the eyes of his intellect and understood this concept, so he took the ram- for repentance and sacrifice atone...'