I kept reading conflicting information on this, and I believe I've figured out why. The mouse works fine with Windows 3.1, as well as Windows 3.11 (tested with WFW) -- but only during setup. Once you're able to boot into Windows 3.11, the mouse stops working. The keyboard still works, just not the mouse.

The fix is to change the default machine type from svga_s3 to svga_et4000.

Alternatively, it seems that the S3 virtual adapter will also work if you install drivers for it.

I wanted to clarify this in its own thread, to help anyone who might be searching for a solution in the future