...or so I say! They're usually at New Market or any larger battlefield that sports large numbers of men dressed in gray. The scarier ones are dressed in dark blue!
As long as I've been in the hobby, there have been loads of ghost stories tied to events. Not just Civil War ghosts, but ones that seem to go along with the reenactment. Being the skeptic that I am, I suspect where you have loads of reenactors roaming around a battleground at all hours of the night, you'll have the ghost stories to match.
Jonah Begone, who has an inexhaustible vault of Civil War stories and opinions, has a couple of "watered-down" ghost stories on his site. Another fellow relates his experiences at a WW2 reenactment in Virginia, a story that is typical of most reenacting ghost stories I hear. A poster at Civil War Talk adds into the discussion about the strange and supernatural. Gettysburg seems to be a magnet for non-reenacting Civil War ghost hunters according to the poster on this forum.