Hi there Matt-omed
and welcome to the madhouse that is EuroKClub!
You don't say how old your K12 is, but living in Switzerland (which is a bit hilly in places) I wonder if you have ever had any problems with the fuelling on your bike. There is a whole pile of pists about poor fuelling and although mine was a pig when I bought it, a new airbox and ICV with the attendant ECU re-flash soon fixed that, along with a (possibly not needed but bought and fitted by then) Power Commander III.
The first time I crossed the Alps en-route to Greece two years ago, I had 'orrible fuelling problems at altitude. Every time I climbed the bike began to hang at high revs on the run into hairpins and then stumble and hesitate on the way out, not nice really
As soon as the bike dropped back to 'normal' altitude, everything returned to normal till the next time it climbed when it did it all over again.
It did exactly the same thing in the Italian Alps last year but behaved itself at lower altitude in the Picos in Spain this year.
Brian (who can't find any where high enough in UK to check this feature out)