When the order between zig and zag is exchanged, does it still mean the same, as "zag when others zig" in the second example ?

It does; it's like there is no difference between "you are the yang to my yin" and "you are the yin to my yang" or other pairs of complementary objects. (Granted, there are some semantic differences between yin and yang; but let's assume us Westerners have only the vaguest ideas what those are exactly.)

While zigging and zagging is the normal order of the expression, I don't think it would matter in this particular twist on the phrase to say that Montana is zigging while others are zagging, or vice versa; the implication would be the same.

@Tim (1) There is NO usual order of expression. Both are completely common (as is the case with all "pair word common and/or humorous phrases" in English. (2) there is absolutely NO difference if one order or the other is used. (It's also quite common to use both humorously: "He zigs when others zag and zags when others zig.")

@Fattie There certainly is a usual order for native speakers. This kind of format is (generically) called ablaut reduplication and the order of vowels is generally from the front of the mouth to the back. It's understandable if you say it the other way but it feels very awkward.

@user3067860 with issues of "what does a native speaker say" (sometimes the "regional variations" comes in to play), it sometimes comes up that 2 native speakers here on the site disagree on "what is common". Not much can be said in such cases. What you say about "i-first" tuples, good on you for raisin' the issue, applies to king-kong adjacent sounds. In the idiom at hand, the whole humorous point/origin is that you separate such a pair and put them in a long sentence and fool with them; nevertheless you raise a great point ("the original hyphen word the whole thing is a play on is..."), sooo

@Tim further to my comment just above. Due to the outstanding point by user306, let me clarify a bit more: The idiom is based on the word "zigzag" which, of course, is in the order "zig" then "zag". When you use the idiom ("He shoulda dun zagged when he zigged!") there is NO DIFFERENCE AT ALL in meaning if you go one way or the other: note that in BOTH CASES you are "making a joke on" the original word (zigzag). IMHO

@Fattie What you're saying is not counter to what I said but agrees with it: My words: "I don't think it would matter in this particular twist on the phrase to say that Montana is zigging while others are zagging, or vice versa; the implication would be the same".

I think the phrase is less about being unpredictable and more about doing the opposite of the crowd such as being buying stocks while everyone else is selling. If you are merely unpredictable, you might do the same thing as everyone else or you might not. There are other phrases that are a better fit for being unpredictable such as 'wild card'

I think an underrated part of this answer is "can, as everyone knows". I would really struggle to explain the difference in "has that ability" vs "has the ability" and I think you got it exactly right.

@JimmyJames I think "has that ability" is not as definite as you're making it out to be. It's not saying that Montana always acts contrary, only that they can be contrary.

@TimR I didn't mention that part of it. Are you referring to Kaia's comment?

@JimmyJames Your comment that "the phrase is less about being unpredictable and more about being opposite of the crowd" needs to take into account the entire phrase, not just the zigging and zagging part: "Montana has that ability to zag when people zig". The zig/zag implications are indeed as you say, going opposite the crowd, but "has that ability" means that they can go counter to the crowd, and "that ability" implies that they've got a reputation for doing so, but it doesn't mean that they always will do so.

@TimR "but it doesn't mean that they always will do so." It also doesn't imply unpredictability. Saying that someone zigs when others zag doesn't mean they will always do so. It just means they don't always follow the crowd. Maybe crowd members perceive this as unpredictable because they expect everyone to follow the herd but from the zagger's perspective, it's not about being unpredictable, it's about taking advantage of the foolishness of the herd. Or that's what it means to me, at least.

I think this answer is the clearest. But I think it's also worth noting that, when coming from a political operative in this context, all it really means is "we're not giving up hope."

To the "no difference between zig and zag" I would add that to many they are nonsense words; I have also heard the phrase "You herped when you should've derped" for instance. The point is, there are multiple possible options, and it's left up to context to decide what is meant. The exact meanings of zig and zag are mostly irrelevant, except that they're verbs.

@JakeRobb Well, what it really means is impossible to say. It could mean "If I were to concede to the press at this point in the campaign that we've got a snowball's chance in Montana, my political consulting career is likely to go up in smoke."

@JimmyJames Again, in your latest comment by focusing exclusively on zigging and zagging, you're ignoring the contribution to the meaning that "has that ability" makes here. It is that phrase in combination with zagging when others are zigging that conveys the sense of unpredictability.

@TimR, agreed. The only thing we can really infer from the quote in that context is that they know that it doesn't look good for Democratic Senate seats in Montana, but that they are not willing to (publicly) admit defeat at this time.

@TimR I'm focusing on that part because it's the only relevant aspect for the question. Has the ability to is not required understand the meaning of the idiom. I really have no idea why you think it does.

If we replace the phrase 'to zag when people zig' with 'do something different from everyone else', to make the whole phrase: "“But Montana has that ability to do something different from everyone else.” The idea that "has the abilty to" implies unpredictability or somehow modifies any phrase to imply unpredictability is just not true.

Huh? Show some evidence of your claim. It's absurd.

The question doesn't ask about 'has the ability to' which is pretty straightforward.

"5. Zig When Others Zag. Any pioneer instinctively knows that you won’t win if you always play by someone else’s rules. When everyone is telling you to go one way, take that as a sure sign you need to find another. Remember, what has worked for others might limit your success or stymie your originality."

"Smashing Paradigms - When others Zig, you Zag: In Positioning Strategy, you can either choose to go with the market, or go against the market. If you choose the latter, when others “zig”, you “zag” The degree to which you choose to “zag” though, is very important. You can go slightly away from what everyone else is doing, or you can go radically away.

"What Does "Zig When One Should Zag" Mean? "Zig when one should zag" is an English idiom. It means "to do the opposite of what one should do; to make an error or misjudgment."

"1. Zig When Others Zag The phrase “zig when others zag” is a popular idiom that conveys the idea of taking a different approach or going against the norm. It suggests that instead of following the crowd, one should choose a different path or strategy to stand out or achieve success. The words “zig” and “zag” are used metaphorically to represent opposite directions."

It doesn't mean it's unpredictable, it means it's contrarian.

@MichaelKay To what does "it" refer in your comment, and what is the subject of the first sentence in my answer? The recent series of comments disputing my answer have tunnel-vision.

@TimR, Read my comment as "The remark about Montana zagging when others are zigging does not mean that Montana is unpredictable, it means that Montana is contrarian". (I'm afraid my comment duplicates what many others have said. I should have read more carefully.)