I identified the problem by using the -d option on mingw32-make.

The debug information showed that mingw32-make was using sh.exe to create a new process for gcc, and sh.exe isn't included with mingw-64. You have to install msys2 to get the unix-style commands, which include sh.exe.

After installing msys2 and adding c:\msys64\user\bin to the path, mingw32-make started working.

According to this post, https://superuser.com/questions/1258498/how-to-start-the-shell-in-mingw-64 it is stated in the documentation that these commands are not included... but I am not very diligent about reading documentation :-(