The decision
You've got the argument and the method. What's left is to decide, and I'd like the decision to fit in one sentence.
When I notice the turn, I say so in the same conversation.
Three parts.
The first is the noticing, from chapter 20. The step down to a weaker argument, the reach for their tone, the "well, anyway." That's the signal, and the signal is the whole cue. You're not deciding whether you're wrong, which is a decision the turn has already made for you. You're noticing that it's been made.
The second is the sentence, from chapter 21 or 22 depending on size. Five words for the roundabout. Three sentences for the supplier. Then the beat of silence, and nothing after the full stop.
The third is the scope. The same conversation. Not later, not privately, not in a corrected version of the story next week. If the turn comes late, the rule becomes the next conversation, and chapter 25 covers that. But the default is now, because now is when it costs one minute and later is when it costs an evening.
There's a form of planning that helps with rules like this, and it's been tested many times. Peter Gollwitzer and Paschal Sheeran reviewed ninety-four studies of it in 2006. You decide in advance what you'll do and when, in the form "when this happens, I'll do that," and people who plan that way follow through much more often than people who only hold the intention. So write three.
When I catch myself reaching for a weaker argument than the one I just made, I'll stop and say "I was wrong about that."
When someone shows me a figure or a fact that changes my view in a meeting, I'll say what I thought, what changed and what I think now, before the meeting moves on.
When I've climbed down and the other person says "told you," I'll say nothing and let it pass.
What to expect. This is my expectation and not a finding. The first week, you'll notice the turn about half the time and act on it less than that, and the times you do act on it will feel worse than they look. The minute of heat will be a full minute. By the second week the heat will be shorter, because you'll have learned that the beat of silence after the five words gets filled by the other person and not by the ceiling falling in. Somewhere in the first month, someone will climb down to you, unprompted, about something small, and you'll realise it's because you did it first. The number of second arguments will fall, because there'll be fewer first arguments left open to feed them. Phillippa Lally and colleagues, following 96 volunteers who were forming a new daily habit, found it became automatic over weeks and months rather than days, and that missing a day didn't set it back much. Expect the same shape. Slower than you'd like, and forgiving of a bad Tuesday.