Imitation candle devices and systems with features enable simulation of a realistic candle flame using moving lights are disclosed. In one aspect, an imitation candle device is provided that includes a flame sheet shaped to resemble a flame, a support member positioned in proximity to the flame sheet, and a light casing including a hole. An end of the support member extends into the hole and a tip of the end of the support member is in contact with an inner wall of the hole to allow movement of the light casing on the support member. The imitation candle device also includes a light emitter enclosed at least partially in the light casing and movable with movement of the light casing. The light emitter is oriented at an inclined angle with respect to the flame sheet to emit light onto the flame sheet.