I just did a fresh install of my Cougar on a new PC running Windows 10.
Here is exactly what I did, in sequence:
Installed Falcon 4.0 from the original CD.
Installed BMS 4.35.
Installed the Cougar driver (Windows Vista x64) in administrative mode. (Right click on installer, run as administrator)
When the driver installer told me to connect the Cougar, I did. It detected.
And that was it.
It showed right up in BMS in setup, controllers, joystick.
That was all I needed to do.
There is a lot of control configuration left to do, but that’s all I had to do to install the Cougar and get BMS to see it.