Well, I have managed to solve my own problem, although this may still be useful to others.....
I discovered that when going via the "Test" button to open the "Test Joystick Buttons" window with the "Waiting" message, the joystick button press would not be recognised until I pressed the Reset symbol. Silly me.
Once I pressed "Reset", it recognised and reported the joystick button immediately.
Problem solved and I can move on now!