Finally got to the bottom of the problem. I'd been purposely clicking for two seconds on empty space on the home watch face. It actually requires that you click for two seconds on the hours and minutes display in the center. Doing that allowed me to access the custom watch face, so I can now see what I'm doing.
How to show custom Wear OS watch face on Android Emulator?
My environment is Windows 10 Pro, Visual Studio 2019 Community with the Xamarin Workload installed. I've set up one device in the device manager: Wear OS round for 9.0 (Pie) using the Intel x86 image.
I followed the instructions on this page https://learn.microsoft.com/en-us/xamarin/android/wear/platform/creating-a-watchface?tabs=windows to get a sample watch face built. I can build, deploy it to the emulator and "run" it but all it does is display the stub "Hello World" application.
That's the expected initial behavior, it takes the steps under the "Try it!" heading to actually show the watch face. Except that's where things fail. Swiping right in Step 1. works and takes me to what I assume is the emulator image home screen, but Step 2 fails: clicking and holding for two seconds or more on the emulator watch face has no effect whatsoever: no amount of swiping either left or right gets me to a list of watch faces.
So what do I have to do in order to display my newly built watch face?