Murder Mystery on a Train (American book)

I woke up yesterday unable to think of anything but this book I read when I was about 7. I have no idea of the title and from memory, when I tried to find out more about it back then, it was a hard book to track down.

The title had something to do with "moon" or “midnight"

If you know what the book is, but haven't finished it, don't read the last paragraph.

Please. Pretty please. It is a murder mystery set on a train. I am unsure of the decade, but one of the characters keeps referencing knowing Florence Nightingale. It is an American book, I think southern.

The main character comes across a body in the dark room of a train. The victim was burned with some kind of chemical. So bad that it melted through to the bone.

The killer was eventually found because earlier in the book they had been wearing their trousers over their boots "as in the modern fashion", but after the cuffs had been melted by the chemical they had tucked them back into their boots.