I'm curious whether it is permitted to work on a tourist etc type visa when you're in Germany on a non-work visa, when you are only visiting temporarily on vacation, but your employer asks you to take your laptop and work for some of the time. 

What does German immigration authorities have to say about that? As in - if you bring your laptop and declare expressly at the immigration counter that you're here on vacation and going to work part time for your employer back home will they tell you to go get a work visa? If not, how many hours are permissible? 

1) If you are on tourist visa, you are not a tax resident. To be a tax resident, you will have to be staying in this country for may be 180 days atleast. Tourist visas are valid usually for 90 days. On tourist visa, you are not allowed to work in Germany. If you were tax resident, you would have to declare the income earned overseas.

2) You are not allowed to work at all on tourist visa. If you declare that you would be working on tourist visa for outside Germany, they your need for tourist visa may be questioned. I have not read German immigration laws in detail, I feel t should not be a problem.