Tjunkaya is a member of the Pitjantjatjara people. She was born in the desert in the far northwest of South Australia. Her mother had walked from Walytjitjata, in the Northern Territory, and arrived at Ernabella Mission at Pukatja or Ernabella shortly after Tjunkaya's birth. Ernabella was run by missionaries at the time, and Tjunkaya grew up there. The craft room at Ernabella Mission was established in 1948 and nurtured the artistic talents of Tjunkaya and other children and adults living on the Mission. The craft room taught spinning and weaving originally but later added batik and painting to its activities, and later still became a professionally run Aboriginal-owned incorporated arts enterprise known as Ernabella Arts after the Mission was closed and the land returned to its traditional Pitjantjatjara owners. 