Tribal Gaming Eligibility Act - Amends the Indian Gaming Regulatory Act to place restrictions on the conduct of gaming on lands taken into trust for an Indian tribe after October 17, 1988, as part of the settlement of a land claim, initial reservation of a newly recognized tribe, or restoration of lands for a tribe that has its federal recognition restored.

Prohibits gaming on such lands, with specified exceptions, unless the Secretary of the Interior determines that the land is eligible for gaming and the tribe demonstrates: (1) a substantial, direct, modern connection to the land as of October 17, 1988; and (2) a substantial, direct, aboriginal connection to the land. (The Secretary and the state in which the gaming is proposed can still allow gaming on lands acquired for a tribe after October 17, 1988, if they concur that it is in the best interest of the tribe and its members.)