If idle shake or rattle totally went away when raising engine, cause might be engine mount only.
Mine vibrated badly whenever engine was running but worse in idle when the left engine mount was collapsed. Replaced left mount with a Lemforder for my vehicle and all abnormal engine shake went away. Maybe the 1 yr old mount collapsed early because of oil softened the mount or because it is not a good brand and rubber softened.
In addition, collapsed engine mount caused PS belt to touch the oil cooler hose. Vibration told me to do the repair before something else failed.