This is track number 6 (closing Side A) from Les Baxter’s 1963 album Soul of the Drums. This albums was one of Baxter’s last in the exotica genre and is pretty good overall.
Unfortunately, “Mai Tai” is maybe the least exotic song on the album, and was described by Ambient Exotica (reprinted in The Les Baxter Companion, 2018) as a “stupefying silkened string panorama.” Since this album was Baxter’s first on Reprise it also means that none of its tracks made it onto the otherwise excellent Capitol Records compilations from the 1990s.