Some of mine will only eat if I leave the rat laying on the ground for them. They just seem to prefer it now for some reason. They generally prefer the quiet and 1 or 2 will only eat in the middle of the night hours after I've left it for them and closed up.
Taking a while to find the head is not uncommon for some of mine either.
You can leave the rat laying there overnight without issue. It won't decompose so much it causes problems in 8 or 10 hours.