What I do, is I have the ghost die immediately on the first night.
The Ghost observes everything during the night, and the last thing I do that night is ask the ghost to write down the 10 letters.
I believe this works quite well
This is also what I do. I have also sometimes made the first player eliminated by any means into the Ghost. This helps the first player eliminated not feel like he got screwed out of playing. When doing it this way, I hand them a card to write their ten letters on, and collect it after the first full night they were able to observe.