She began by studying singing and music in Sydney in the 1930s, but after attending a performance of the Bodenwieser Ballet in 1940, she immediately decided on a career change to dance.
[2] Her father, a car salesman, began showing signs of alcoholism when Kramer was about 10, leading to her mother leaving and secretly relocating with the children to the suburb of Coogee when Eileen was 13.
[2] In 1936, when her mother remarried, Kramer left home and lived in a shared cottage on Phillip Street until 1940 and studied singing at the Sydney Conservatorium of Music.
[9] After leaving the troupe in 1953, Kramer travelled to India, then lived and worked in Paris as an artist's model, often for André Lhote and his studio.
[2] While working on their film in the mid-1960s, Shadmi had a stroke, and Kramer effectively put her dance career on hold for 18 years while caring for him in New York.
[9] In 2017, she created a dance-drama A Buddha's Wife, inspired by her travels in India, part of a wider work celebrating her life, and supported by the Arts Health Institute.
The music was inspired by Greek mythology, modernist poet Rainer Maria Rilke's Sonnets to Orpheus, and Pike's personal experience of grief.
Dancers Nadiyah Akbar, Josh Freedman, Benjamin Hancock, Taiga Kita-Leong, and Siobhan Lynch star in the film along with Kramer.
[3] Kramer later had two extended relationships while living abroad, with Baruch Shadmi (1920–1987) and "rich Southern widower" William "Bill" D. Tuckwiller (died c.2013).