What types of signs are given by the "lights in the expanse of the heavens"?

The ancients, not knowing anything about astrophysics and related information, took note of their surroundings, including the stars/planets (I don't know if they differentiated between them). For example, if there were a supernova that were dramatically visible from Earth, people would instantly understand it, being very unusual, as a sign in a similar way that they might take other unusual natural events (tornadoes/hurricanes/storms, floods, great fires, droughts, solar eclipses(?), etc.) as signs from heaven. Frequently, such signs were taken to be warnings from God. God assigns some of those kinds of things to himself as means of judgment/punishment of Israel. (Jonah; Ps 107; 2 Sa 21:1; etc.)

Regarding astrology, the wise men followed a star (or something bright) to find the young Jesus (Mt 2:1-12). Perhaps they were coincidentally wrong about astrology but managed to find Jesus anyway, but there's at least a suggestion that they knew what they were doing. Though they probably weren't Jewish, one might think that if God didn't want people assigning meaning to the stars in some fashion, he might not have made it so the wise men used that method. Perhaps astrology isn't the same as "divination" or "soothsaying", or at least there's a method or motivation for using it that would distinguish that act from being something God prohibited.

I might start by questioning whether "signs" means what you seem to think it means, or whether it's an artifact of the translation—something that might be better hashed out on BH (I couldn't find any reference to it there). I'm just noting that different translations give for this passage various equivalents; for example:

• "let them be for signs and for seasons and for days and years" (NASB, and with varying use of commas, also KJV, Douay-Rheims, Darby, RSV, and a few others)
• "Let them serve as signs to mark sacred times" (NIV)
• "They will serve as signs for festivals ..." (Holman Christian Standard Bible)
• "Let them mark the seasons, the days and the years ..." (New American Bible, Revised Edition)

What "signs", exactly, are referred to here may depend on the proper interpretation of the word your translation gives as "signs". This is worth asking on BH.

This What is the Authoritative Catholic Explanation of why the Magi get a pass, yet Catholics are to reject Astrology?, seems to be related to this question.

God Has Spoken by His Son Hebrews 1:1-4 (RSVCE) 1 In many and various ways God spoke of old to our fathers by the prophets; 2 but in these last days he has spoken to us by a Son, whom he appointed the heir of all things, through whom also he created the world. 3 He reflects the glory of God and bears the very stamp of his nature, upholding the universe by his word of power. When he had made purification for sins, he sat down at the right hand of the Majesty on high, 4 having become as much superior to angels as the name he has obtained is more excellent than theirs.

If there is True Religion [and there is since there is the One, True God], it seems that there must a graduation from 'no religion' (doubt there is such a thing) to the one , true Religion, from bad and corrupt religion to the good religion. Compare with good science vs. bad science. I do not know what the total process was when the Amerindians cured Malaria with quinine. In addition to administering the medicine, perhaps there was some superstitious ceremony involved.

I do believe that there is science in the stars, that there are signs to be read there as per Genesis 1:14-16 (RSVCE). My take is that it belongs to the primitive religion, perhaps the religion Man practiced after expulsion from Gan Eden, perhaps a religion revealed by the angels but apt to corruption since there are competing angels (good vs. fallen; fallen vs. fallen). Scripture seems to suggest a connection between angels and stars.

The prohibition in Israel and the Church can then be explained this way: if one has the superior, purer religion, why dabble in the primitive one admixed with superstition that may lead one astray?

This is what contributed to my thinking:

When the Egyptian pagan priests intended to read the stars, they fasted as a preparation, performed certain purifications, clothed themselves in sackcloth, and sprinkled themselves with ashes. While they gazed upon the stars from their tower, sacrifices were offered. The pagans of those times had a confused knowledge of the religious mysteries of the true God which had been handed down from Seth, Henoch, Noe, and the Patriarchs to the chosen people, therefore there were so many abominations in their idolatry. The devil made use of them, as later on of heresy, to weave the pure, unclouded, authentic revelations of God into a snare for man's destruction. Joseph and Aseneth | The Life of Jesus Christ and Biblical Revelations | Anne Catherine Emmerich

and an excerpt from Angels | New Advent:

And it is not a little remarkable that only two verses later he warns his readers not to be seduced into any "religion of angels". He seems to put his seal upon a certain lawful angelology, and at the same time to warn them against indulging superstition on the subject. We have a hint of such excesses in the Book of Enoch, wherein, as already stated, the angels play a quite disproportionate part. Similarly Josephus tells us (Bel. Jud., II, viii, 7) that the Essenes had to take a vow to preserve the names of the angels.

Probably the most well known light sign in the sky was the announcement of the birth of Jesus:

All Scripture is quoted from the King James version unless otherwise stated.

Matthew 2:1 and 2 Now when Jesus was born in Bethlehem of Judaea in the days of Herod the king, behold, there came wise men from the east to Jerusalem, Saying, Where is he that is born King of the Jews? for we have seen his star in the east, and are come to worship him.

Another fairly well known is:

2nd Kings 20:8 through 11 And Hezekiah said unto Isaiah, What shall be the sign that the LORD will heal me, and that I shall go up into the house of the LORD the third day? And Isaiah said, This sign shalt thou have of the LORD, that the LORD will do the thing that he hath spoken: shall the shadow go forward ten degrees, or go back ten degrees? And Hezekiah answered, It is a light thing for the shadow to go down ten degrees: nay, but let the shadow return backward ten degrees. And Isaiah the prophet cried unto the LORD: and he brought the shadow ten degrees backward, by which it had gone down in the dial of Ahaz.

Jesus himself pointed to others:

Matthew 16:3 And in the morning, It will be foul weather to day: for the sky is red and lowring. O ye hypocrites, ye can discern the face of the sky; but can ye not discern the signs of the times?

Luke 21:11 And great earthquakes shall be in divers places, and famines, and pestilences; and fearful sights and great signs shall there be from heaven.

and

Luke 21:25 And there shall be signs in the sun, and in the moon, and in the stars; and upon the earth distress of nations, with perplexity; the sea and the waves roaring;

There are numerous passages in the Old testament which allude to the Sun, Moon, Stars, and even Constellations being used to indicate some happening caused by God; here is just one example:

Isaiah 13:9 through 11 Behold, the day of the LORD cometh, cruel both with wrath and fierce anger, to lay the land desolate: and he shall destroy the sinners thereof out of it. For the stars of heaven and the constellations thereof shall not give their light: the sun shall be darkened in his going forth, and the moon shall not cause her light to shine. And I will punish the world for their evil, and the wicked for their iniquity; and I will cause the arrogancy of the proud to cease, and will lay low the haughtiness of the terrible.

To list them all would make an excessively long answer.

There is a definite difference between trying to foretell an unknown future and seeing things unfold and knowing what's going on. I don't have to be a meteorologist to know that when dark clouds start gathering overhead there's a chance it might rain.

A good representation of this is in Revelation:

"I watched as he opened the sixth seal. There was a great earthquake. The sun turned black like sackcloth made of goat hair, the whole moon turned blood red, and the stars in the sky fell to earth, as figs drop from a fig tree when shaken by a strong wind. The heavens receded like a scroll being rolled up, and every mountain and island was removed from its place. Then the kings of the earth, the princes, the generals, the rich, the mighty, and everyone else, both slave and free, hid in caves and among the rocks of the mountains. They called to the mountains and the rocks, 'Fall on us and hide us from the face of him who sits on the throne and from the wrath of the Lamb! For the great day of their wrath has come, and who can withstand it?'" (Rev 6:12-18 NIV)

Having read this, you would not have to be an astrologer to realize that when the sun goes black, the moon turns blood red and heavenly bodies start crashing to the ground that the sixth trumpet has sounded. It's already been foretold in the Bible. You're just recognizing the signs when they come to pass.

Seeing a sign for what it is isn't the same as trying to divine the future. Divination is trying to see the unknown. We've already been told in the Bible what to watch for.

We are to be watchful and alert. Jesus said there would be signs and that "when these things begin to take place, stand up and lift up your heads, because your redemption is drawing near." (Luke 21:7-31 NIV)