DAYTON, Ohio — In the hours before the mass shooting, Connor and Megan Betts, brother and sister, drove together in the family’s 2007 Corolla to visit this city’s historic Oregon District, an area alive on a summer night with restaurants, bars and nightlife. Then, police said, they separated. It is not clear what the woman, 22, did at that point. But her brother, 24, donned a mask, body armor and ear protection. Wielding an “AR-15-like” weapon with magazines containing 100 rounds, he set out on a street rampage that, while it lasted only about 30 seconds, claimed the lives of...