Yes, everything connected correctly. The GT5 registers the brake, but not others. Do I need to make any initial set up?
You can check the firmware version on the wheel.
...but you need windows to test the CSPs, and to update the firmware on the wheel if that has to be done.
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Not needed.
Just check if the connector is not plugged in to the shifter port instead of the pedals port at the back of th wheel.