GAFFNEY, S.C.—It is no simple matter to keep the nation’s most recognizable and giggle-inducing water tower as pretty as a peach.

The “Peachoid” sits high above Interstate 85 in Gaffney, S.C., and brightens the lonely four-hour stretch between Atlanta and Charlotte for tens of thousands of drivers a day. Its round shape, warm tones and indentation between halves drive some drivers to anatomical distraction, including a character on Netflix’s “House of Cards,” who crashed on an episode of the show while texting, “Doesn’t the...