Turn the camera off before connecting to USB.

That simple.

I eventually went through the manual page by page & that was the only thing I hadn't done.

Switch it on again once connected, then CCP will immediately identify & connect to it.
Whether you connect before or after launching CCP appears to make no difference.

Once connection has been established for that session, it then appears you can re-connect at any time & it will still be recognised - it's just that first time.

Needless to say, it was one heck of a "D'oh!" moment. I just hope it may be of some help to future Googlers.

This was tested only on Mac & only on a D5500.
I could not repro reports of it not working if other USB devices are connected. I always have at least half a dozen other things permanently connected. It may require that the camera tether goes on its own bus - i.e. connect straight to the computer, not through a hub.

I would appreciate confirmation (or otherwise, with details) of it working on Windows or with other Nikon cameras.