If I may interject: How about a sense of the passage of time? I'd call it the ultimate minimum requirement for an inner narrative that can be recalled. In other words, we can't really say we were conscious during some interval unless we remember there being an interval. Note that this isn't equivalent to memory in general, since we can certainly recall facts that have no "timestamp".
Well, that's interesting. Tell me what happens in you when you sense the passage of time.
I'm recaling an interesting experiment I read about a long time ago, so it would be quite a challenge to google it, so here it is from memory.
A group of scientists asked subjects to estimate the passage of time. Say, to press a button after they felt 5 minutes elapsed. After this control test, they showed the subjects a miniature room, like in a doll house, and asked them to estimate the passage of time in that room, pressing the button again after 5 minutes in the miniature room elapsed. They found the subjects scaled the passage of time to match the size of the room, e.g. pressing the button after 2:30 for minutes sensed to have elapsed in a half-sized room. I'll be thinking about what that means to the consciousness of the passing of time.
I suspect there is some machinery in the brain that clocks out time. Maybe it's partly a sense of the sum of our breaths or heartbeats. Many people always have music playing in their heads. That might help.
If a machine needed to sense the passage of time, a clock would be added as, again, an input device, as there is one in most every computer today. I don't doubt the brain/body has a few timers analogous to the clocks in laptop computers.
Indeed, there's been a lot of progress in discovering the biological clocks in people, other animals, and plants. I encourage you to google this yourself if you are interested.
I'm finding that confidence that the mind arises from a machine makes solving it mysterious almost trivial.
Before I forget, is a person who's lost the sense of time definitely not conscious?
For that matter, is a being lacking an inner narrative not conscious, either?