The "time of the gentiles" being the "Day of the Lord"

 A near and far wrath may be seen in Luke 21:

²⁰ "But when you see Jerusalem surrounded by armies, then know that its desolation is near. ²¹ Then let those who are in Judea flee to the mountains, let those who are in the midst of her depart, and let not those who are in the country enter her. ²² For these are the days of vengeance, that all things which are written may be fulfilled. ²³ But woe to those who are pregnant and to those who are nursing babies in those days! For there will be great distress in the land and wrath upon this people. ²⁴ And they will fall by the edge of the sword, and be led away captive into all nations. And Jerusalem will be trampled by Gentiles until the times of the Gentiles are fulfilled.

²⁵ "And there will be signs in the sun, in the moon, and in the stars; and on the earth distress of nations, with perplexity, the sea and the waves roaring; ²⁶ men's hearts failing them from fear and the expectation of those things which are coming on the earth, for the powers of the heavens will be shaken. ²⁷ Then they will see the Son of Man coming in a cloud with power and great glory. ²⁸ Now when these things begin to happen, look up and lift up your heads, because your redemption draws near."   Luke 21:20-28

Jesus foretold the desolation of Jerusalem as the wrath of God on Israel. I believe this was in AD 70 by the Romans; it was a near wrath. He said Jerusalem would be trampled by gentiles until "the times of the gentiles be fulfilled." I believe this "times" is DOL, when the nations are judged and Jerusalem is delivered. Jesus then gives more detail of DOL in the text that follows. This whole text may reveal both a near time of wrath (AD 70) and the far-final wrath of God (DOL) in the prophetic vision of Jesus.  And from the time of the near wrath to the time of the far wrath, Jerusalem with be trampled underfoot.  That trampling will come to an end when the times of the Gentiles is fulfilled, being the Day of the Lord (the coming of Christ to judge the nations at the end of the great tribulation).

Ezekiel prophesies of the near wrath to come upon Egypt and the nations allied to her. This would also be through the instrumentality of Nebuchadnezzar of Babylon: Thus says the Lord God: I will also make a multitude of Egypt to cease by the hand of Nebuchadnezzar king of Babylon. 30.10 

Ezekiel 30.1-3 is a prophecy of the DOL that appears to look beyond the near future (God using Neb to judge Egypt and her allies) to the far future (the DOL on all the nations) in its terminology.

Ezekiel says it is "the time of the Gentiles": Wail, Woe to the day! For the day is near, even the day of the Lord is near; it will be a day of clouds, the time of the Gentiles.

Some translate this as the "time of the doom [or distress] of the gentiles." I suppose this is because the LXX has the word "end" instead of "time." And the "time" in view here is the eschatological judgment of the nations. Jesus prophesied of Jerusalem being trampled underfoot by gentiles "until the times of the gentiles are fulfilled." I don't know if the plural of "time" is significant, and I suppose most would say this is a reference to the dominance of gentile world powers, but it could be a reference to DOL. Jerusalem will be trampled by gentiles until the time of the end (or the doom or the distress) of the gentiles. That time will be DOL.

It would seem that Jesus was referring to what Ezekiel presented as the backdrop of Egypt's judgment from God through Nebuchadnezzar. Charles Feinberg writes: "The reference here is best taken as God's judgment on Egypt identified in principle with that day when He will call all nations into account. Some have interpreted the significant phrase ["day of the Lord"] to mean any time in which God’s judgments are experienced on earth. Although such an interpretation will allow for all the references to be included under it, nevertheless it empties the words of their well-known eschatological force. They do speak of events in the far future when God will consummate His plans for Israel in the earth." The Prophecy of Ezekiel by Charles Feinberg

many shall run to and fro at the time of the end

Daniel 12:4 says to "Seal the Book until the time of the end." This must signify that the prophecy of Daniel is complete and must be secured and not altered.   It's fulfillment and understanding will be the time of the end, being that time of trouble referenced in Daniel 12:1 (I believe  is the "Great Tribulation" of which Jesus spoke). This does not mean we do not read it and seek to understand it.   But how all the events will play out will be best discerned as they happen. 

Daniel 12:4 says that "many shall run to and fro and knowledge shall increase."    I know that some believe this speaks of our age of modern travel and internet access to information, but I believe this refers to the increase in understanding of prophetic Scriptures in the time of the end, for those who seek it. 

"To and fro" appears several times in the Old Testament (see *below) and just speaks of going back and forth.  

There will be many who will seek out the word of God to understand what's happening, and these will be the "wise" ones of Daniel 12:10:  "Many shall be purified, made white, and refined, but the wicked shall do wickedly; and none of the wicked shall understand, but the wise shall understand."

Compare this understanding with Amos: "12 They shall wander from sea to sea,

And from north to east; They shall run to and fro, seeking the word of the LORD,

But shall not find it." Amos 8:12 

In Amos, we see that the word of God is in view, but in that case, they will seek but not find.  

But in the time of the end, many will go here and there seeking the word of God, and they will understand.

* Then he sent out a raven, which kept going to and fro until the waters had dried up from the earth. Genesis 8:7

 For the eyes of the LORD run to and fro throughout the whole earth, to show Himself strong on behalf of those whose heart is loyal to Him. 2 Chronicles 16:9

And the LORD said to Satan, "From where do you come?"
So Satan answered the LORD and said, "From going to and fro on the earth, and from walking back and forth on it." Job 1:7 2:2

 Will You frighten a leaf driven to and fro?
And will You pursue dry stubble? Job 13:25

He breaks open a shaft away from people;
In places forgotten by feet
They hang far away from men;
They swing to and fro. Job 28:4

And Your plunder shall be gathered
Like the gathering of the caterpillar;
As the running to and fro of locusts,
He shall run upon them. Isaiah 33:4

​"Run to and fro through the streets of Jerusalem;
See now and know;
And seek in her open places
If you can find a man,
If there is anyone who executes judgment,
Who seeks the truth, Jeremiah 5:1

They run to and fro in the city,
They run on the wall;
They climb into the houses,
They enter at the windows like a thief. Joel 2:9

And the man who stood among the myrtle trees answered and said, "These are the ones whom the LORD has sent to walk to and fro throughout the earth." Zechariah 1:10

There are a few more.