Are you meaning that there is a mountain pass and that the border goes through/runs through this pass?
A pass is likely to be fairly short and not particularly winding. If you were talking about a border that was partly defined by the course of a river, you would say, the border follows the river.
A 'notch' is a small nick, like a knife would make if you sliced a piece of wood in the same place a few times - like a very shallow v-shaped marking.
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