I've seen this question asked on other sites and believe it or not, we discussed it at NASK (2016) in the advanced class. There was some disagreement on whether seĝo means the whole throne or whether it can refer to just the seat (the movable ring that you sit on.)
Where there was agreement, though, was that neceseja seĝo clearly and unambiguously refers to the whole appliance, not just the seat. Myself, I learned truseĝo for the seat. Others suggested sidilo - which I always understood as an expression meaning "back side."
Is there any consensus on this question?