Try to select "Joystick". Paradoxically the mouse works nicely that way.
By the way I am experimenting with the Windows JoyToKey joystick emulator, so that I can use a joystick under Windows which translate into a mouse under Basilisk II, with excellent results.
It's a complex tool, with many options. I had to limit maximum excursion and set the "spring mode". Unfortunately it works only with Basilisk II in window mode, not full screen. You have to center Basilisk II window on Windows desktop as good as possible, so to limit joystick and mouse offset when the cursor is supposed to be at the center of the scren.