According to 19 U.S.C. § 1581, what should a vessel do if hailed by a customs officer?

When hailed by a customs officer, the appropriate action for a vessel is to stop and prepare for a document check. This requirement is grounded in the authority granted to customs officers to conduct inspections and verify the documentation of vessels to ensure compliance with laws regarding customs and immigration.

Stopping allows customs officers to board and inspect the vessel in question, which is crucial for maintaining maritime security and enforcing regulations. Upon stopping, the vessel's crew must be ready to present necessary documentation, such as proof of registration and cargo manifests, to the customs officials.

The other options do not align with the legal expectations set forth in 19 U.S.C. § 1581. Igniting signal flares might signal distress but would not fulfill legal obligations to customs officers. Hailing back with a registry number does not meet the requirement of halting for checks, and attempting to evade capture by increasing speed contradicts the vessels' obligation to comply with law enforcement.