Yes, the Sadducees were "in charge" until after the Temple was destroyed when the Pharisees took over. However, both groups were on the Council.
Yes, both groups were on the council. "Groups" speaks in terms of
sects. Moses did not speak of
sectarian offices. All that is really there are offices of authority. The Judges, and the priests. The high priest was the head of the court, and the ruler of the people. We see this in Paul's writings. Letters from the high priest were his authority to go and find those of the way for punishment. He does not cite a sect or a sectarian head. The high priest is always the source. Josephus says that Levites were always present even in the lower courts. That the offices, became sectarianized, does not mean the offices were based on that. And....Josephus says that often times when in positions of authority, they addicted themselves to the
notions of the Pharisees, otherwise the people would not tolerate them. So Moses seat may have been Pharisaical in that sense.
The seat of Moses.
Num 9:6 And there were certain men, who were defiled by the dead body of a man, that they could not keep the passover on that day: and they came before Moses and before Aaron on that day:
7 And those men said unto him, We are defiled by the dead body of a man: wherefore are we kept back, that we may not offer an offering of the LORD in his appointed season among the children of Israel?
8 And Moses said unto them,
Stand still, and I will hear what the LORD will command concerning you.
Moses did not judge as an expert in what he already knew, or had taught....... Moses had to go and consult God for the answer.
De 33:8 And of Levi he said, Let thy Thummim and thy Urim be with thy holy one, whom thou didst prove at Massah, and with whom thou didst strive at the waters of Meribah;
Kings enquiring for answers:
1Sa 28:6 And when Saul enquired of the LORD, the LORD
answered him not, neither by dreams, nor by Urim, nor by prophets.
Ezra, Nehemiah Scribes and prophets.......
Ezr 2:63 And the Tirshatha said unto them, that they should not eat of the most holy things, till there stood up
a priest with Urim and with Thummim.
Ne 7:65 And the Tirshatha said unto them, that they should not eat of the most holy things, till there stood up
a priest with Urim and Thummim.
Just a side thought.
Will modern dna results suffice replace these, to have priests eat of the holy things if a third temple is built?