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A set \( S \subseteq V \) is a dominating set of a graph \( G = (V, E) \) if each vertex in \( V \) is either in \( S \) or is adjacent to a vertex in \( S \). A vertex is said to dominate itself and all its neighbors. A set \( S \subseteq V \) is a \emph{total dominating set} of a graph \( G = (V, E) \) if each vertex in \( V \) is adjacent to a vertex in \( S \). In total domination, a vertex no longer dominates itself. These two types of domination can be thought of as representing the vertex set of a graph as the union of the closed (domination) and open (total domination) neighborhoods of the vertices in the set \( S \). A set \( S \subseteq V \) is a \emph{total, efficient dominating set} (also known as an \emph{efficient open dominating set}) of a graph \( G = (V, E) \) if each vertex in \( V \) is adjacent to exactly one vertex in \( S \). In 2002, Gavlas and Schultz completely classified all cycle graphs that admit a total, efficient dominating set. This paper extends their result to two classes of Cayley graphs.