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.

Key Inclusion Criteria:

1. The participant weighs greater than equal or to (≥)40 kilograms (kg) and has a body mass index (BMI) between 16 and 38 kilograms per meter square (kg/m^2) [inclusive].
2. The participant has a documented, current diagnosis of NT2.

Key Exclusion Criteria:

1. The participant has a current medical disorder associated with excessive daytime sleepiness (EDS) other than NT2.
2. The participant has medically significant thyroid disease.
3. The participant has a history of cancer in the past 5 years. (This exclusion does not apply to participants with carcinoma in situ [such as basal cell carcinoma] that has been treated and is stable, or who have been stable without further treatment. These participants may be included after approval by the medical monitor).
4. The participant has any of the following viral infections based on a positive test result: Hepatitis B surface antigen (at screening), hepatitis C virus (HCV) antibody (at screening), human immunodeficiency virus (HIV) antibody/antigen (at screening).
5. The participant has a clinically significant history of head injury or head trauma.
6. The participant has history of epilepsy, seizure, or convulsion (exception for a single febrile seizure in childhood).
7. The participant has a history of cerebral ischemia, transient ischemic attack (<5 years from screening), intracranial aneurysm, or arteriovenous malformation.

Takeda provides access to the de-identified individual participant data (IPD) for eligible studies to aid qualified researchers in addressing legitimate scientific objectives (Takeda's data sharing commitment is available on https://clinicaltrials.takeda.com/takedas-commitment?commitment=5). These IPDs will be provided in a secure research environment following approval of a data sharing request, and under the terms of a data sharing agreement.

IPD from eligible studies will be shared with qualified researchers according to the criteria and process described on https://vivli.org/ourmember/takeda/. For approved requests, the researchers will be provided access to anonymized data (to respect patient privacy in line with applicable laws and regulations) and with information necessary to address the research objectives under the terms of a data sharing agreement.