On my Ti-nspire CX II, the on.paint function only runs when I click the page number. It works fine on the student software.

I won't pretend I know how this really works, but the way I see it the paint function is called when events are triggered, and also when platform.window:invalidate() is called. You can add this code and it should refresh automatically without input:

timer.start(0.01)
function on.timer()
        platform.window:invalidate() --refreshes screen
end

Be warned about using this method though, switching off the handheld while the timer is running will cause it to freeze.