So I assume du hast noch immer eine Schwyzer Reisepass?

IN your ´home´country you are only allowed 2 days of travel (for OUT and IN). If you can live with that, you can simply let it be. No conductor will go and ask if you actually live not in that country-this  can (not necessarily will) of course happen if this is different.

IF not, then indeed only the serviceteam can settle this-there is a special form for that and you MUST indicate for which date is should be settled-they are very busy and try to work in that order. And likely as CH you will know that tickets there cost an awful lot of frankeli and thus conductors will indeed see official proof that you do not live in the land of Heidi & mountains.

Hey Thanks for your answer, it’s very useful!
I do need to travel more than once in the land of Heidi :/

I already submitted a request with customer support, but I did not mention the departure date. Should I submit again? 

That's probably best. Mention an exact date. Saying it's "urgent” doesn’t help either because people have very different opinions about what that means.

Unfortunately we can't update your country of residence after you've purchased the Pass. This can only be done by ordering a new Pass with the correct country of residence and requesting a refund for your old Pass (a Pass exchange).