I think this is exactly it, but let me ask another question (which is not rhetorical, I really don't know). Does the fact that one can describe what consciousness is and where it came from in humans help them to detect it in non-human and/or non-biological entities?
That is a really good point. Yes, I think function is diagnosis on this.
Constant self-awareness, self-experience, self-focus, self-management, and self-improvement of one's own self (mind), is going to be an adaptive behavior for anything intelligent with resources to leverage. Whether truly independent, or highly motivated to serve others. The mind is the greatest tool.
I think that is more than simply a good functional definition of consciousness. How could all that integration and self-integration not be conscious.