State boundaries in mountainous regions

I have in front of me a map of South-East Europe (as depicted below) from the inside cover of the 1967 German edition of John Stoye’s The Siege of Vienna. A detail shows three then dukedoms situated to three sides of the Carpathian mountains: Transylvania to the West, Moldavia to the East and Wallachia to the South.

What is interesting to me is that one sometimes finds this pattern (different territorial domains on different slopes of a mountain range), whereas sometimes one finds the inverse (a single territorial domain with a mountain range at its center). The latter e.g. seems to be the case for the former princely county of Tyrol in the Alps (also pictured below), for modern Switzerland also in the Alps), and possibly for Georgia-and-Azerbaijan (both form parts of the Ciscaucasus and Transcaucasus respectively), Lesotho (“the only independent state in the world that lies entirely above 1,000 metres”), Timor-and-East-Timor, Haiti-and-Domenican-Republic, Guatemala-and-Belize and Honduras-and-El-Salvador vs. Nicaragua and Costa Rica, Norway-and-Peru (the latter two at least partly to both sides of major coastal mountain ranges.

I am wondering whether there is any systematic rule which may determine whether a given region will likely host one pattern or the other. For instance, if there are different cultures and languages from previous migrations on both sides of the divide, this clearly favors the first pattern; if there is a local important pass connection over the mountainous region, this may favor the second option (e.g. the case with the Gotthard Pass in the Swiss Alps, but certainly not universal: e.g. the Khyber Pass connects Pakistan and Afghanistan).

Are any such rules apparent from the study of human history (as well as geography)?

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(dukedoms of Transylvania, Moldavia, Wallachia in the 17th century)

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(princely county of Tyrol; notice the west-east main ridge of the Alps and the resulting a north-south drainage divide)

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