Rothenburg, Steinach, Munich, Innsbruck train(s)

Being a tight wad my tendency would be to wait for the next train if did not have to be at the hotel at a certain time. I guess you should just book your ticket from Innsbruck to Steinbach.

I wouldn't worry about it. the Rothenburg “train” shuttles back and forth between Rothenburg and Steinach and has no other purpose than to take passengers to / from the onward trains in Steinach.
And it has a time cushion of 15 minutes at both endpoints to compensate for delays of the connecting trains. The four-minute transfer time is perfectly adequate, it's been that short for as long as I can remember, and that's quite a long time.

As you can see the train shuttles back and forth between Rothenburg and Steinach every hour, 20 minutes travel followed by 10 minutes wait time for passengers at each end. As such, there is some flexibility to wait if an inbound train at Steinach is a few minutes late, or a passenger needs extra time to make the transfer. There are no other trains on the line to worry about conflicting with.

...connection time at Steinach is only 4 minutes...10 minutes wait time for passengers at each end...

We went from Wurzburg to Rothenburg with a connection in Steinach. Much to our surprise, the train in Steinach waited for the passengers on a train from another location that had been delayed.

No need for a taxi for the last leg.

Thanks all! Great to get 1st hand knowledge. I'll skip the taxi and take the train.

These connections are timed. So those 4 minutes basically mean: The train leaves 4 minutes after the train it connects to has arrived. The train conductor will not leave until everyone has made their transfer.

Think relay race, and you are the baton.