Tezcatlipoca

Tezcatlipoca (テスカトリポカ) is a Magic God of Aztec Mythology and a member of the true Gremlin, first mentioned in Shinyaku Toaru Majutsu no Index Volume 13.

Etymology
(often translated as 'Smoking Mirror' from Nahuatl) is a major god in Aztec Mythology, associated with obsidian, the night, jaguars, sorcery and strife, among other things. He is said to have cooperated with Quetzalcoatl to create the world from the body of the monster Cipactli, losing his foot in the process. He is also said to have acted as the First Sun but was knocked from the sky by Quetzalcoatl and destroyed the world in anger, in the form of a jaguar. He also caused the ends of the three following worlds before the current world and the Fifth Sun.

Appearance
While Tezcatlipoca's appearance hasn't been described during an actual appearance by him, a fake version of him formed by Sample Shoggoth appears as a brown man with dark-colored hair in dreadlocks and a black, polished round mirror in place of a leg.

Magic God Invasion Arc
At some point around the time of the incident instigated by the High Priest, Tezcatlipoca encountered Kamisato Kakeru and was 'exiled' by his World Rejecter.

Salome Arc
Tezcatlipoca remains exiled, but his likeliness was used in a bluff by Kihara Yuiitsu while fighting Kamijou Touma, Salome and Misaka Mikoto, making use of Sample Shoggoth and an attenuated St. Germain virus to make imitations of the Magic Gods and their magic, to make them think she could draw out the Magic Gods and their power after stealing World Rejecter from Kamisato Kakeru.

Character Art Design
According to Haimura, there weren't any particular details focused on in the designs of Tezcatlipoca and the Magic Gods whose appearances were shown for the first time through Yuiitsu's fabrications, given their lack of mention in the story.