I enjoyed reading this. The whole thing felt like a kind of delightful gory romp. I can visualise all the ghosts vividly. Your first paragraph is doing beautiful work. It sent me off in the wrong direction (body of dead girl in bath) before delivering the surprise.
Other things I loved:
The ghost with the cravat making Neil think he looked like a poet.
The sentence ‘Public executions – butchers.’ is gorgeous. I particularly love the rhythm.
Historical ghosts. I love that some go that far back.
The fact that he’s making a ghost map so he can plan his route around them.
The thing growing by the bins. I’m intrigued. You’ve made me believe this is going to be important.
The humour in general.
When are we in time at the start? It’s ‘Late August’ later, but that means no time is given for the time when he first sees the ghost.
Which town/city is Neil living in?
After the very lively beginning, I felt pace in the first chapter began to flag, particularly in the long sequence from the first knock at the door to his letting Caro in. (I have similar first chapter issues, so I recognised them.)
In the scene where he sits down to discover what the ghost is thinking, it wasn’t clear to me at first that these were her thoughts, not his.
The two images of Caro are each strong, and as the ‘past’ one came first, it stayed in my mind’s eye. The dreadlocks won over the bob.
Smaller details (though not to an Agatha fan!):
As you named the first Agatha Christie he saw, I think you need to name the fourth one too. (How’s your Agatha knowledge? I had issues)
So that’s it. Hope this was useful, and well done on being brave enough to post.
By the way, I loved that the cat is called Fosco!