Ms Eaton was reported missing by friends on 2 July after going on a run.
"According to his claims, he placed the victim, unconscious, in the trunk of his auto and transferred her to a ventilation drain in the wartime storage (tunnel), where after raping her, abandoned her there".
After leaving her body there, he re-blocked the entrance of the shaft with a wooden palette and then went to a nearby graveyard, "where he carefully cleaned the trunk of his auto from evidence and other forensic findings", Papathanasiou said. He got married three years ago and is the father of two young children.
Over the weekend, local police brought in 10 possible suspects after collecting DNA that pointed to these individuals, all of whom lived in the area. Chilling details allegedly shared by the suspect were released by Papathanassiou, who says the man claimed that after seeing Eaton he hit her two times with his auto to stop her and then put her in his trunk.
The man said, according to the police, that he hit her twice with his auto to render her unconscious before placing her into his trunk to transfer to the abandoned WWII-era bunker, which he entered via a ventilation shaft.
Police also said evidence pointed to a struggle between the two before Eaton was ultimately killed before having her body dumped in the abandoned bunker. They added that the motive appeared to have been "sexual abuse". Her body had substantial injuries from a knife that was "defensive" in nature, the source said. The elderly farmer told the newspaper that he recognised her from the photos and described the clothes she was wearing to the police. They also requested data records from local mobile phone companies in hopes that they may identify the person or people who left Eaton's body in the bunker.
Eaton, 59, had been attending a conference in the city. Eaton's husband and two sons had traveled to Crete aid in the search. Her remains will be returned to the United States for burial.