waiting for a single tile to complete a pair and win; waiting for one tile to finish a pair with four melds already completed
Mahjong term: a tenpai pattern where the hand needs only one specific tile to form the final pair (head). The first gloss describes the general case; the second describes a specific situation where all four melds are already complete and only the pair is missing.
I declared riichi with a single-tile wait for the pair.
He stayed on a single-tile wait for the pair and never drew that tile until the end.
Compound of 単騎 (single horseman, here meaning 'single' or 'alone') and 待ち (waiting). The term is specific to mahjong.