Add a subrule to the rule Ghosts named Ectoplasm. Set its text to

When a ghost chooses a villager’s house to haunt, if the ghost has not chosen a house to haunt in the last 24 hours, one item called Ectoplasm shall be placed in the inventory of the villager whose house is haunted. When a ghost stops haunting a villager’s house, one Ectoplasm (if there are any) will be removed from their inventory. A villager who has at least one ectoplasm in their inventory may privately ask a villager with a Religious occupation to remove one Holy Water from the inventory of the asked religious villager as well as one ectoplasm from the requesting villager’s inventory. If the villager with the religious profession agrees, the villager with the religious occupation shall privately mail the Mayor of the fact and remove the said objects from the proper inventories.

Add the following sentence to the end of the subrule Religious Occupations:

As a daily action, a villager with a religious occupation may produce one inventory item called Holy Water.

This allows people to possibly know whose haunted, a way to hide the fact to a degree, and has safeguards against abuse in place to prevent things like a ghost choosing lots of targets and ectospamming the town.