Im a bit confused as to why you think it is the Northern kingdom which marked the timing of when the gentile times began. The northern kingdom had a king, but he wasnt located in Jerusalem...the seat of the Throne of David - which is representative of Gods kingdom.
The northern kingdom did not represent Gods rulership because they had turned apostate. It was only in Jerusalem that Gods throne was located and therefore it is only that part of the kingdom which is relevant.
You are confused because Ezekiel didn't say that. Did you read the passages I quoted or not?
God divided the kingdom and put the two parts each under their own period of judgment. The period of time for the northern kingdom was explicitly distinct. Therefore, its beginning point would pertain to it's destruction.
Also, as regarding relevance, Aholibah (Judah) would also be given the cup of her sister Aholah (Samaria) at some point as well. That happened in 70AD.
Assyria destroyed the northern kingdom, but Jerusalem continued to have a king reigning on Gods throne right up until it was destroyed by Nebudcadnezza in 607bce.
That is beside the point as far as the northen kingdom's period of judgment is concerned. The period of judgment for the southern kingdom starts when it was destroyed, which as you mention was 587bce.
The prophecy of Ezekiel stated that the king would be removed from Gods throne (which was in Jerusalem) and THAT would mark the beginning of the gentile rule.
Ezekiel 21:26 ‘Remove the turban, and lift off the crown. This will not be the same. Put on high even what is low, and bring low even the high one. 27 A ruin, a ruin, a ruin I shall make it. As for this also, it will certainly become no [one’s] until he comes who has the legal right, and I must give [it] to him.’
There isn't an explicit time I am concerned about with regard to when the Gentiles actually began to rule. The only reason they can come to rule is because Israel shall have been scattered among them. The point of the material I have presented is to show when the dispersed of Israel would be eligible to regain self-rule because their judgment is expired. This is bedrock. You cannot say the explicit judgment God gave to the northern kingdom didn't start until the southern kingdom was destroyed. That's a train off the tracks.
Also, your passage makes a reference to Shiloh, which can be understood as 'asher-lo' or "to whom it belongs". This is a reference to the birthright tribe of Joseph. When the northern kingdom is eligible to be out from under their judgment, that is the time when the Shiloh Messiah can come, which is the time the scepter departs from Judah and goes back to the birthright tribe. That individual shall be a descendent of Jesus, David and Jesse, which is to say he shall possess the Holy Grail. In this way God's promise to David is honored as well as the birthright being honored.
Your welcome to apply it to the Northern kingdom, but i really cant see how it could be correct ...especially considering the judean tribes were also scattered and spread about, some going into captivity in babylon and many more being dispersed into the surrounding nations.
Ezekiel was very clear. Each split of the kingdom had their own distinct period of dispersion with its own duration being prescribed. Both of the adulterous sisters were "stoned to death". And, the southern kingdom got it again in 70AD when her sister's cup was given over to her as the Lord said He would do. This is why Jesus was unable to manifest the kingdom in victory at that time. Aholibah had a brief period of eligibility as her shorter period of judgment had expired, but God knew she must receive her sister's cup so the karma (for lack of a better word) she gave herself assured she would be destroyed again. Once she rejected her Messiah from Judah, she was handed her sister's cup, which means she was lumped in with her sister to finish out her sister's cup with her.