Sleeping
My mother (90) goes in phases. During my last visit, (I live at the other end of the country so go to stay every couple of months) I think she was only awake about 25% of the day. She herself was disconcerted by how tired she was. But this happens in phases: there is no constant, regular pattern.
She always sleeps twelve hours at night, but she has long phases of being alert and restless during the day. And during these phases she can walk fairly long distances, or arrive on my sister's doorstep very many times (my sister lives a couple of streets away). In fact, we wish she wouldn't be quite so active, because on some of her restless walks she disappears and doesn't come back for a long time because she's forgotten where she is and where she's going. We have a UPS device on her keys, but sometimes she forgets her keys. And taking her for a walk doesn't work in itself by tiring her ready for a snooze, because during the restless phases within half an hour she's forgotten we've been for a walk and is ready to go for a walk etc etc.
We wonder whether the phases of sleeping nearly all day are connected with a progression of the illness, whether another bit of brain damage has occurred, and she's sleeping in a valiant attempt to repair the connections. All her life she has slept whenever she was ill, and now is no exception.
Sadly, she is easier, in many ways, when she is so sleepy. Her restless phases, especially when she keeps wanting to pack her things and go home (she lives in her own home) are harder to deal with, both practically and emotionally.
I agree that stimulus helps, that there is a kind of sleepiness connected with boredom that the right kind of stimulus can improve. But I'd say that during her sleepy phases our mother sleeps in a different way from that dozy boredom thing. A way of sleeping that's more like half-coma -- a different consciousness from ordinary sleep. She doesn't seem to be ill -- no other symptoms -- but she gets confused when she wakes up because the sleep is so deep, that when she wakes she sometimes thinks it's morning and time for breakfast.
I think as far as possible it's best for people to do what they need to do: sleep if they are sleepy, and walk miles if that's what's required. The difficulty is providing an environment in which people can comfortably and safely do what they need to do.