The picture above, from the New York State archive, is labelled “New York City, 98th Street”. It seems more like Brooklyn than Manhattan because of the lack of bigger apartment houses interrupting the lines of the almost-rowhouse-sized walk-up apartments. Besides the title, there are two ways to identify the exact location: the elevated train running over the next avenue in the distance and the very tall and slender tower. If we were on the east side, there would be two elevated visible, the Second and Third Avenue lines. On the west side, the Sixth and Ninth Avenue lines shared tracks north of 59th Street. That led me to a 1902 map of West 98th Street, and there’s the tower, at the corner of a boiler plant for the Croton water system.
The tower served the same purpose as the water tanks on top of tall buildings: providing local storage of water so that the adjacent buildings had sufficient pressure. The Croton aqueduct as a whole has a fairly regular slope down from High Bridge to the south, and natural pressure is sufficient for low buildings on most of Manhattan island. (Keep in mind that when the system was planned in the 1840s, there only were low buildings in Manhattan.) Where there are hills, the natural pressure would not be enough, so towers were built. Water was pumped up to a tank at the top of the tower – almost certainly one reason for the boilers present in that building – and that gravity-fed back down to serve the local hill-top buildings.
So that tower only existed to meet the needs of the people in the nearby blocks and, like most infrastructure, was probably ignored by everyone as long as it functioned properly. The construction of the Delaware and Catskill water systems in the early 1900s made the towers unnecessary. The building was there until the early 1950s, but the tower had been demolished earlier. It was gone before the 1940 tax photo of the lot was taken, for example.