Narcolepsy without cataplexy or Narcolepsy Type 2 (NT2) is a lifelong condition that makes people very sleepy during the day, regardless of how much sleep they get at night. People with NT2 may fall asleep suddenly, have trouble staying awake during the day, or may not be able to sleep well at night. They may have difficulty thinking clearly, paying attention, or remembering things, during the day. These symptoms can make daily activities like driving, working, or caring for their families challenging, impacting their quality of life. Orexin is a chemical made in the brain that helps keep a person awake and alert. TAK-360 acts like orexin. Previous studies have shown that medicines that act like orexin may keep people awake. The main aim of this study is to learn how safe TAK-360 is and how well adults with NT2 tolerate it. Researchers also want to find out if TAK-360 can help people with NT2 stay awake and determine the right dosage needed to do that. Participants will be randomly (by chance, like drawing names from a hat) assigned to get either TAK-360 or placebo in the treatment period. The placebo is a pill that looks just like TAK-360 but does not have any medicine in it. Using a placebo helps researchers learn about the real effect of the treatment.