I did some restoration work in a previous life as a Master Carpenter on a house that sounds somewhat similar to the house you speak of.
The “water box” in the attic "Attic was bigger than most houses!), actually served the house water system through an extremely complex series of pipes and joints. IThe house had been built in the mid 1850’s (so I understood) by a Founding Father of the area who owned just about every business and thing around.
The water was loaded into a tank from the rivers nearby, brought up to the house and emptied into the tank using some sort of pump. The water flowed from the tank into the house using gravity.
It was an extremely intersting set up and house.
Unfortunately the house was mostly destroyed by fire a few years after I finished on it.
AND NO I did not burn it down, it was hit by lightning!