Mongolia Third Neighbor Trade Act This bill allows the President to provide duty-free treatment for certain apparel and textile articles imported from Mongolia. This duty-free treatment expires on December 31, 2029. The President must annually monitor, review, and provide a briefing to Congress on (1) the implementation of this duty-free treatment, (2) Mongolia's compliance with the eligibility requirements described in the bill, and (3) U.S. trade and investment policy with respect to Mongolia.