Taxi to Reutte in Tirol from Fussen

We are planning an overnight stay in Fussen and will travel to Garmisch / Zugspitze the next morning. It looks like taking the S7 train is the fastest route from Reutte, but I would need to take a car or bus from Fussen. The buses are an hour apart and we would have to wait 30 minutes in Reuttein. We would rather take a taxi and have a shorter wait, if possible. Will taxis go from Fussen to Reutte?