Do fish sleep ??
Do fish sleep with their eyes open ??
Actually, they don't have eye lids, only a membrane. Or rather they have transparent, always-closed eye lids.
But they do sleep.
To wake up a sleeping human
Now we human beings can close our eyes but not our ears. So our ear can hear but our brain cuts it out when we sleep. So, it is possible that our neighbour can scream and the scream can reach the brain and shake up the senses and wake a person up. But any amount of visual impact in front of a sleeping person cannot wake him/her up as the eye lids are closed.
To wake up a sleeping fish
BUT, fish cannot close their eyes. So technically if we show some disturbing visual stuff to sleeping fish it must reach the brain and shake it up and wake up a fish, right ?
Waking up a mermaid
Now that's interesting. May be she has a pair of batting eyelashes with her eye lids, and also membranes. Lucky her. :)