She was killed with the garotte. Death was by strangulation. The garotte was found tied around her neck and looped around her wrist. The blow to her head was post mortem. A baseball bat was found in the alley behind the house. The idea of the flashlight was posited because the depression at the front of her skull matches the shape of the flashlight.
Thai Sticks
Schiller says that there are facts about the murder weapon not known. Why would you be surprised? Many facts are kept secret.
What was used as the garotte, how was it tied, where exactly was she left, in what physical position, did the killer add or subtract anything from her clothing, etc. There is a lot of detailed information only the killer could provide.
Will be interesting to see how the confession stands up to the Kerr family's claimed alibi.