MAYORAL FEAT In April, while the average stir-crazy citizen was binge-watching “Tiger King,” Pete Buttigieg took a different tack: He started writing a book. First, the former presidential candidate and two-term mayor of South Bend, Ind., converted a guest room into a study. Then he woke up early every morning and got to work, snacking on peanuts and almonds while his dogs, Truman and Buddy, dozed nearby. (His husband, Chasten, was putting the finishing touches on his own future best-selling memoir, “I Have Something to Tell You,” in the dining room.) By late July, Buttigieg had finished a draft of “Trust,” which debuted at No. 11 on last week’s hardcover nonfiction list. His first book, “Shortest Way Home,” was also a best seller.