What makes the "Nuclear Option" in the US Senate a precedent that its chair has to uphold?

Question

Let me first sum up what the nuclear option is, as far as I understand it : a cloture vote happens, carrying more than half of the votes but less than the required supermajority. Pursuant to the written rules of the Senate, the chair announces that the cloture vote fails. A senator makes a point of order invoking a rationale not written in the senate rules. The chair rules against that point of order. An appeal is made on that ruling, and is ruled on by a majority of the senators (potentially with the VP tie-break). The ruling is overturned and the cloture is invoked.

It makes sense that the "thing" on which cloture gets invoked (let's say the nomination of Neil Gorsuch to the Supreme Court for example) does get the cloture, as the Senate as a whole ruled that way. But how and why would the rationale invoked by the Senator raising the point of order (here, that SCOTUS nominations' clotures are by simple majority vote) be kept for future rulings, as it contradicts the written rules of the Senate ? Why is that rationale considered a more important precedent than the rules ? Do the written rules say that an overruling of the chair does such precedent ?

Further question, assuming such thing is not part of the written rules. What would happen if a future chair (let's say the president pro tem, with the VP not present but agreeing with them) decides to only uphold the written rules of the Senate, accepting individual challenges of the ruling of the chair but rejecting the idea that such challenges create precedents ? What would they violate, apart from the opinion of the parliamentarian ?

NB : it may seem that this is a partly theoretical question, in part due to the very partisan nature of senate chairing and rules enforcing. However, there are a lot of people, among which the senators themselves, who recognize these precedents as real existing things. In particular, there have been a lot of judicial nominations since Reid's nuclear option and several SCOTUS nominations since McConnell's, and in all cases the chair applied the precedent as created (apparently) by the nuclear option. Instead of requiring individual overrulings of the chair for individual nominations, for example.

Answer 1

It is a precedent that the chair has to uphold because the Senate says so.

When the "nuclear option" was first used, to allow cloture on appointments by simple majority this question was asked of the Chair. The chair gave the opinion (presumably on advice of the Parliamentarian) that upholding the point of order did indeed create a new precedent (and announced that fact to the Senate). This opinion was challenged and put to a roll call vote. The senate voted (52-48) that a new precedent had indeed been set.

The precedent becomes part of the rules of the Senate.

Now suppose in future there is a cloture vote on an appointment, and it passes 52-48 (say) If the chair rules that this isn't enough there would be a point of order and the 52 votes would again overrule the chair. This is why it is a "nuclear option", it is difficult to modify this precedent and re-establish the 60 vote requirement, as whenever a point of order could arise, there would always be majority short term interest in maintaining the precedent.