The word 'eidetic' was coined around 1924 and is derived from the German eidetisch, a term used by psychologist Erich R. Jaensch, who did pioneering research on visual acuity and memory, and based on the ancient Greek word eidos meaning image, form, or shape. 'Eidetic memory' later became popularly known as 'photographic memory' and 'total recall'.
This was more than a century after the process of photography ('drawing with light') was discovered and at least 80 years after the term 'photograph' had first entered into popular usage.
Therefore 'eidetic memory' predates 'photographic memory' but not the process of photography itself.