Use that continues while the cooler should be idle can point to a feed or level-control issue, but the equipment design must be known.
Do not climb to roof-mounted equipment or open powered equipment to diagnose it. An accessible feed valve, visible drip, or ground-level overflow observation is enough to prepare a useful call. Plumbing and HVAC work may need different scopes or qualifications.
Keep this boundary: Do not cap a drain or overflow simply because it releases water. Its purpose and the manufacturer's design must be understood first.