Also to clarify, I think that the Hebrews defined by culture as being Syrian can be seen as a point where some of them defined their tribes based on a matri-lineal origin starting with either Leah, Rachel, Bilhah or Zilpah, but the Matriarchal aspect was, at times, a contention due to the Canaanite presence that they had been dealing with.
For example, the story of Solomon and his mother presents one of many stories of how that Matriarchal head government contended with the kings of Israel.
Solomon fell in love with, Abishag, the Black Virgin that became a nurse for David. He was one of the shepherds that was part of the party go and find a nurse and as he was assigned in that region in the mountains of Lebanon for a season, he party found Abishag and brought her back to the Capitol in Mt. Moriah. But once there, Solomon's mother revealed that she had a bad spirit and shocked Solomon.
After the death of David, Solomon wanted to marry Abishag and he pursued her. But his older brother became enraged that David intercepted him and gave the kingdom to Solomon and therefore, he plotted against Solomon. He went behind Solomon's back and asked Bathsheba to give him Abishag. And Bathsheba then surprised Solomon one day and told Solomon to give Abishag to his older brother Adonaijah. Bathsheba ordered the life of that young girl to be given away as if she was a slave and WOW! Her dark nature was revealed. Solomon could not believe it because, as he mother too is black skinned and he knew what she endured due to Colorism, he could not believe that she would try to destroy the life of another Black skinned beauty. So Solomon told his mother, 'you are going to make me a slave to my brother--and I am the king'.
But as Bathsheba was the Queen of queens, as David's wife, Solomon did not cross her, but what he did was have his brother killed.
So after that, he married Abishag, and Bathsheba went down in shame.
Later, when Abishag was older, she co-authored the love story between her and Solomon that became the Book Song of Solomon.
This book Song of Solomon became the rendition of the famous fairy tale we know today as Cinderella.
Bathsheba became the 'evil step-mother' syndrome and her name was also written out of the GOSPEL. She was written in as 'the wife of Uriah-the-Hittite'. She was written out of the Bible, even though it is Bathsheba, that is the matri-lineal basis of both Joseph and Mary! From David and Bathsheba, the lineage of Jesus' parents came!
So in conclusion, the Matriarchal system did contend with the kings of Israel from time to time due to the Canaanites, the Hittites and other Asiatics old civilizations that had infiltrated the western world of Ham whereby women would challenge the patriarchal systems. Another dramatic historic event of this contention was the story about Ahab and Jezebel.