Aboriginal Australians carefully observe the properties and positions of stars, including both overt and subtle changes in their brightness, for subsistence and social application. These observations are encoded in oral tradition. I examine two Aboriginal oral traditions from South Australia that describe the periodic changing brightness in three pulsating, red-giant variable stars: Betelgeuse (Alpha Orionis), Aldebaran (Alpha Tauri), and Antares (Alpha Scorpii). The Australian Aboriginal accounts stand as the only known descriptions of pulsating variable stars in any Indigenous oral tradition in the world. Researchers examining these oral traditions over the last century, including anthropologists and astronomers, missed the description of these stars as being variable in nature as the ethnographic record contained several misidentifications of stars and celestial objects. Arguably, ethnographers working on Indigenous Knowledge Systems should have academic training in both the natural and social sciences.