I have just purchased a used Jacuzzi spa. How can I determine if the ozonator is working or not?

It depends on the type.

Of ozonator that is. It'll either be one that uses a UV style bulb where you can see the light when it's turned on, or a CD (corona discharge) type where there may be a corona indicator window that will illuminate when it's powered up.

Otherwise, the last resort is that you should easily be able to smell the ozone when the filter cycle is on.