Most of us expect clear judgment to show up when it counts. The serious moment arrives, a crisis or a sudden choice, and we assume the right response will be there on cue. Often what turns up instead is an instant reaction.
One teacher, closing the course, compares it to music. Nobody walks onto a concert stage cold. You prepare, you rehearse, and then the performance can be a beautiful one. The pause works the same way. Practise it on small things: rather than saying yes or no straight away, a thought comes, you pause, ask 'should I, should I not?', and then act.
Then the real moment comes. The teacher's example is happening upon a car accident and suddenly being involved. Without the practice, the reaction comes on its own, and maybe it's right, maybe it isn't. With it, you go inside for a moment and ask what to do now, and the answer, the teacher says, comes through clearly. The hard part is that the small rehearsals feel pointless. Nobody needs a pause to decide on a second coffee. That is exactly why they're safe to practise on.