The Samerburg service station on autobahn A8 south of Munich seems a good option for hitching from here to Innsbruck in Austria as shortly after it, the A12 heads south to Austria.
But picking up lifts going to Innsbruck from here might be difficult as the vast majority of traffic is heading for Munich.
Best advice: look for Swiss plates for cars that might be heading through Innsbruck to Switzerland or, better still, Austrian ones. Approach drivers in the rest stop and ask them, in German preferably, if they are heading to Innsbruck. Be prepared for it to take time though.
If this doesn't work out, try to hitch a sympathetic ride into Munich that will drop you at the entrance to the A95 to Garmisch and from there hitch village by village over the border into Innsbruck.