If your Swiss Travel Pass is still valid on the day you leave for Austria you only need to buy a ticket from the border station to your destination in Austria. You do not necessarily need an Eurail Pass.
So just go to www.oebb.at and buy a ticket Buchs (SG) to Salzburg. Maybe look up Zurich (or wherever it is in Switzerland you are starting) to Salzburg on line first, and take a note when that train calls at Buchs, so you can book the correct ticket.