Earlier quoted context omitted.
CPU load (brain activity) while idle would do as a decent first hurdle that seems to meet your requirements. E: Ooh, another one for you. Has the ability to communicate without being prompted first.
What stops you from arguing that it simply died after it accomplished its purpose?
If we're going towards the idea that the AI sentience is being born and dying inside one response I don't think that can be considered sentient (by my earlier definition) as there's no idle time to measure idle brain activity.
It's a bit of a cop out response I know, I'd have done better if I could.