So the installation is perpetually stuck and neither progresses nor completes.
However despite plugging in the Mouse's USB connection to the computer, the installation is unable to continue because the 'NEXT' button remains ghosted-out and the User is unable to click the 'Next' button. When installing Mad Catz RAT 9 Drivers, some may encounter a problem where the driver installation program will 'STOP' at the point it asks you to plug in the Mouse via its USB connection (Wireless receiver USB connection in the case of the RAT 9 gaming mouse). (This may work for some of their other gaming mice such as the RAT 7)
Finally I found a way how to install Mad Catz RAT 9 Drivers which were causing so many problems for some when trying to install.