Re: my cat's eye
The one time Rookie had a slow blink like you're describing, it was after she had been anesthetized at the vet. They put a gel in their eyes while anesthetized so their eyes won't dry up, and apparently the blinking later has to do with the little bit of gel left in their eyes.
The vet gave us eye drops for it, which of course we weren't successful getting in her eyes, but the slow blinking did go away by itself within a day or so.
Holly and Murphy