The "Traveler's Gun Rights Act" amends federal law to define "State of residence" and "resident" for firearm transfer purposes, clarifying that an individual can be a resident of multiple states if they maintain homes in each. It establishes specific residency criteria for active duty military members based on their duty station and for individuals without a physical residence, allowing them to use a private mailbox or post office box address. Additionally, the bill updates the National Instant Criminal Background Check System (NICS) requirements, mandating that identification for firearm transferees include a photograph and either a residential address or a private mailbox/PO box address if no physical residence exists.