In the end, signs served that other express purpose - "a sign" to Israel under the Law - that God in His wrath had turned from that nation...
Israel was a sign people under the Law. When they either got things right, or screwed up as a nation per the Law, they could look to the Law for what had been written there as to signs from God as to the fact of either of those two.
Deuteronomy 28:
1. And it shall come to pass, if thou shalt hearken diligently unto the voice of the LORD thy God, to observe and to do all his commandments which I command thee this day, that the LORD
thy God will set thee on high above all nations of the earth:
2. And all these blessings shall come on thee, and overtake thee, if thou shalt hearken unto the voice of the LORD thy God.
3. Blessed shalt thou be in the city, and blessed shalt thou be in the field.
15. But it shall come to pass, if thou wilt not hearken unto the voice of the LORD thy God, to observe to do all his commandments and his statutes which I command thee this day; that all these curses shall come upon thee, and overtake thee:
16. Cursed shalt thou be in the city, and cursed shalt thou be in the field.
17. Cursed shall be thy basket and thy store.
Consider the following famous one from the above, taken out of context for centuries now:
23. And thy heaven that is over thy head shall be brass, and the earth that is under thee shall be iron.
24. The LORD shall make the rain of thy land powder and dust: from heaven shall it come down upon thee, until thou be destroyed.
2 Chronicles 7:
12. And the LORD appeared to Solomon by night, and said unto him, I have heard thy prayer, and have chosen this place to myself for an house of sacrifice.
13. If I shut up heaven that there be no rain, or if I command the locusts to devour the land, or if I send pestilence among my people;
14. If my people, which are called by my name, shall humble themselves, and pray, and seek my face, and turn from their wicked ways; then will I hear from heaven, and will forgive their sin,
and will heal their land.
Signs were a means of God's communicating his pleasure or displeasure with Israel under the Law.
Psalm 74:
9. We see not our signs: there is no more any prophet: neither is there among us any that knoweth how long.
That out of the way, note the following - Matthew 12:
30. He that is not with me is against me; and he that gathereth not with me scattereth abroad.
31. Wherefore I say unto you, All manner of sin and blasphemy shall be forgiven unto men: but the blasphemy against the Holy Ghost shall not be forgiven unto men.
32. And whosoever speaketh a word against the Son of man, it shall be forgiven him: but whosoever speaketh against the Holy Ghost, it shall not be forgiven him, neither in this world, neither in the world to come.
Acts 7:
51. Ye stiffnecked and uncircumcised in heart and ears, ye do always resist the Holy Ghost: as your fathers did, so do ye.
52. Which of the prophets have not your fathers persecuted? and they have slain them which shewed before of the coming of the Just One; of whom ye have been now the betrayers and murderers:
53. Who have received the law by the disposition of angels, and have not kept it.
With that, we read not only of Paul's salvation, but of a shift in focus - Acts 9:
15. But the Lord said unto him, Go thy way: for he is a chosen vessel unto me, to bear my name before the Gentiles, and kings, and the children of Israel:
The order has been turned. And with that, the remainder of the Twelve are given a sign they will later recall when the salvation of the Gentiles without the Law comes into question because it had been prophesied that Israel would be redeemed first, and the Gentiles would also serve under the Law, Isaiah 2:1-5, etc.
That sign give they of the circumcision which believed? Towards their serving as a witness of these things in Acts 15?
Acts 10:
45. And they of the circumcision which believed were astonished, as many as came with Peter, because that on the Gentiles also was poured out the gift of the Holy Ghost.
God changed some things. Albeit, temporarily, as to that nation.
1 Corinthians 1:
20. Where is the wise? where is the scribe? where is the disputer of this world? hath not God made foolish the wisdom of this world?
21. For after that in the wisdom of God the world by wisdom knew not God, it pleased God by the foolishness of preaching to save them that believe.
22. For the Jews require a sign, and the Greeks seek after wisdom:
23. But we preach Christ crucified, unto the Jews a stumblingblock, and unto the Greeks foolishness;
24. But unto them which are called, both Jews and Greeks, Christ the power of God, and the wisdom of God.
1 Corinthians 14:
20. Brethren, be not children in understanding: howbeit in malice be ye children, but in understanding be men.
21. In the law it is written, With men of other tongues and other lips will I speak unto this people; and yet for all that will they not hear me, saith the LORD.
22. Wherefore tongues are for a sign, not to them that believe, but to them that believe not: but prophesying serveth not for them that believe not, but for them which believe.
Romans 11:
11. I say then, Have they stumbled that they should fall? God forbid: but rather through their fall salvation is come unto the Gentiles, for to provoke them to jealousy.
12. Now if the fall of them be the riches of the world, and the diminishing of them the riches of the Gentiles; how much more their fulness?
God in His wrath turned from that nation, to the Gentiles and Israel was now gradually diminishing away as the issue, in His eyes, for a season, once more.
Read Acts 28. With Paul's pronouncement there, the purpose of signs among the Gentiles - for to provoke Israel to jealousy, came to an end.
Though return they will, and with a vengeance, as 2 Thessalonians 2 and John's Revelation make clear.
Study also Daniel's sense of this and its connection with the Law, in his prayer, in Daniel 9.