Good catch, thanks, and sorry for the mistake. US Senate Rule XX “Questions of Order” is here.

The mechanism is:

1) A Senator raises a point of order, contradicting the Senate rule he wishes to set aside. (Can be any rule whatever.)
2) The chair overrules the point of order.

3) The Senator appeals the decision of the chair to the Senate, which overrules the chair by simple majority vote, as happened in the following example from 2013:

Mr. REID I raise a point of order that the vote on cloture under rule XXII for all nominations other than for the Supreme Court of the United States is by majority vote.
The PRESIDENT pro tempore Under the rules, the point of order is not sustained.
Mr. REID I appeal the ruling of the Chair and ask for the yeas and nays.
(48–52 vote on sustaining the decision of the chair)
The PRESIDENT pro tempore The decision of the Chair is not sustained.
The PRESIDENT pro tempore Under the precedent set by the Senate today, November 21, 2013, the threshold for cloture on nominations, not including those to the Supreme Court of the United States, is now a majority. That is the ruling of the Chair.

tl; dr the Senate has a rule that lets them ignore any rule, including the 60-vote filibuster rule, by simple majority vote. (That’s Rule XX, “Questions of order”.)

It follows then that the Senate can pass anything by simple majority vote, but they and the media find it advantageous to pretend otherwise.

You wrote at 6:43 yesterday “The filibuster, or any other Senate rule, can be set aside at any time for any reason by 51 votes…”

Your link — https://senate.la.gov/Documents/Rules/chapter6.htm — is for the Louisiana State Senate, not the U.S. Senate.

The Bulwark crew does a lot of videos. They undercut the group’s message. Last, Kristol, and the rest of the team would like to be authoritative voices from on high, but seeing them on camera makes it hard to take them seriously. If you wonder why some people still believe the network nightly news, production values have something to do with it. Watching Kristol with his oversized earphones or manic Tim Miller trying to attract attention to himself does a lot to undermine the messaging.

One might think he would think more carefully. But I gave up on scientists as reliably critical thinkers a long time ago and the fancy degrees don’t help.

I don’t have a clue what the rules are – other than rules are made to be broken.

From what you are saying—it seems that the recess appointments can easily been done if Thune works with Trump on it.

Like he can have votes “whipped” for Gaetz – and if not enough he can do a recess for Trump…??

Trump is determined to see Gaetz confirmed as AG despite controversies

Yet the president-elect has made clear that he views Gaetz as the most important member of the Cabinet he is quickly assembling…

Trump wants Gaetz confirmed “100%,” a source told CNN. “He is not going to back off. He’s all in.”

Trump wants this…can’t blame him after weak-kneed Sessions – can it be done?

100% wrong.

By Senate rule it takes a super-majority of 60 Senators to end debate and move to an up or down vote on a bill.

This rule about 60 Senators “voting to end debate” can be waived, and has been waived, with only 51 votes according to the rule I quoted, and so can any other rule, and they do it whenever they want to, not just when you hear about it in the news. When they want to be dramatic they call this “nuking the filibuster” and when they want it to fly under the radar they call it “a procedural maneuver”.

Every time the “filibuster has been nuked” it has been nuked by the rule I quoted, with only 51 votes needed.

Here is the transcript of one occasion on which it was done, and note the vote count, 48-52:

[Mr. REID] I raise a point of order that the vote on cloture under Rule XXII for all nominations other than for the Supreme Court of the United States is by majority vote.
[The PRESIDENT pro tempore] Under the rules, the point of order is not sustained.
[Mr. REID] I appeal the ruling of the Chair and ask for the yeas and nays.
(48–52 vote on sustaining the decision of the chair)
[The PRESIDENT pro tempore] The decision of the Chair is not sustained.
[The PRESIDENT pro tempore] Under the precedent set by the Senate today, November 21, 2013, the threshold for cloture on nominations, not including those to the Supreme Court of the United States, is now a majority. That is the ruling of the Chair.

It is a fact that filibuster or any other Senate rule can be set aside at any time by 51 votes, and any narrative that suggests otherwise is false.

“Dems to Biden: Take Action Before Trump Takes Over“—
https://www.newsmax.com/newsfront/donald-trump-democrats-joe-biden/2024/11/15/id/1188231/
Opening grafs:

Democrats are pushing the Biden administration to put safeguards in place before President-elect Donald Trump takes office, including seating as many Biden-appointed federal judges as possible, finding a way to protect generals Trump plans to expel from the Pentagon, and sending money out to Ukraine, among other items, reported the Hill.

“There’s a lot that the Biden administration can do, and I know that they’ve done some scenario planning,” said Rep. Jared Huffman, D-Calif. “It would be a huge political malpractice for them not to anticipate this scenario and have some plans in place.”

Heh…
They’ve worked SO HARD (and lying SO EARNESTLY) over the past eight-plus years ginning up the HATE and the HYSTERIA.
Why should they stop now??
THEY HAVE A COUNTRY TO SAVE…to fulfill their dreams of destruction….

You are confusing a vote on changing or suspending the Senate rules, as well as the number of votes it takes to pass a bill in the Senate, with the Senate rule for the number of Senators who must vote to end debate and move to an up or down vote on a bill. By Senate rule it takes a super-majority of 60 Senators to end debate and move to an up or down vote on a bill. A modern filibuster is simply a vote count that indicates fewer than 60 Senators wish to vote on the bill rather than a continuous talk-a-thon but the principle is still the same. Also note that Obamacare was moved through the Senate (somewhat dubiously) under special provisions in the Senate rules for finance related bills that suspended the filibuster for those bills specifically.