Hi Hopalong and English,
Don't take me as an expert, please, it makes me nervous

...
But English, I expect that what your brother meant was, if you find your MOTHER's behavior unacceptable, don't make her guess ... tell her straight out that you are not going to sit there and tolerate bad behavior. But actually, YOUR behavior (going LC) is a CONSEQUENCE of her bad behavior ... and you don't have to announce what consequences you are going to impose, you just do it. In fact, keeping the N person guessing about what you're gonna do about it probably works better than announcing what the consequences will be! Of course, nothing works really well because they seldom get that they are the problem ... but in some cases, LC as a consequence works enough to make infrequent contact bearable.
Do you know the principles of reinforcement (a la behaviorism)? Operant conditioning works on the principle that whatever behavior is reinforced is more likely to be repeated. Reinforcement can be positive (a desirable response following the behavior) or negative (the withdrawal of something unpleasant). Punishment is the opposite of reinforcement --- behavior that is punished is less likely to recur.
Ns have punished us all our lives for what the rest of the world considers desirable behavior (having a mind of our own, having a life, etc.) and reinforced us for reading their minds and doing what they want. What makes them so confusing is their inconsistency. Sometimes a behavior is reinforced and sometimes it is punished. But, in general, we are all well-trained to pay close attention and try to read their minds, and to try not to make them mad.
Well, it's time to turn the tables. To reinforce the Ns in our lives for being nice and to punish them for being ugly to us. LC or NC is punishment, about the only punishment that is meaningful to them. If you scold them or berate them, or any of the other usual punishments given to badly-behaving adults, they don't get that the punishment really is related to their behavior. They see it as evidence that we're crazy or bad. There is a fundamental disconnect in their minds between their behavior and most of the consequences of their behavior.
The interesting thing is, you don't have to be AWARE of reinforcement or punishment for it to work. SO, since LC or NC is a meaningful punishment to them, they don't have to actually realize you're doing it on purpose. After awhile, subconsciously they will get the message that every time they do X, you don't call for a long time. For relatively mild Ns, sometimes this works.
BUT, IMO, even if it doesn't work, the main point of LC or NC anyway is the sanity and peace of YOU. So you are setting a boundary and if it works to get them to make nice on Christmas or whatever, great. If it doesn't work though, that's fine. The reason you are doing it is for you anyway.
I once announced to my mom that when I shut up and don't say anything, that means I disagree with her. That drove her crazy. However, the backlash of this is that eventually when she really really wanted to provoke me, she would just keep at me and keep at me until finally my temper blew. If I had never announced the meaning of my silence, she might have assumed she was right and let it go.