Simply put, there is no "Presidency of the Jedi High Council"… Rather, there are three distinct levels of council membership:
- Lifetime seats (5)
- Long-term seats (4)
- Short-term seats (3)
All seats were determined/nominated by the High Council itself[*]. This, in combination with the circular layout of the chamber, strongly suggests more or less "equal status" for all Council members, though clearly more elder members such as Yoda were often consulted for their wisdom and experience.
Thus, Yoda is most likely sitting in that particular seat because it was the spot that was open when he was nominated to the High Council, or for some other apolitical reason – practically speaking, Jedi with other significant duties on Coruscant[†] might be placed closer to the door in the event they needed to leave during a meeting. Alternately, given his age, it might well be that Yoda was placed near the door simply to be closer to the bathroom.
[* This is true until the ascension of Anakin Skywalker, who was "propelled" into the seat by the machinations of Chancellor Palpatine during the events of Episode III: The Revenge of the Sith. ]
[† In addition to his place on the High Council, Yoda was in charge of the Jedi Academy on Coruscant. ]
Why does Yoda sit in position number 3 in the council chamber?