Yeah, this one's a weird but documented glitch. Two possible causes.
First, the ice tray is out of position or blocked by something. Unplug the appliance and check if the ice tray moves freely and is seated correctly. Remove any obstruction.
Second, and this is the quirky one, sunlight is messing with the infrared sensor. The ICE FULL condition can't be detected if the infrared light module is interfered with by direct sunlight. Unplug the unit, move it to a place not exposed to sunlight, plug it back in, and press ON/OFF to restart.
If that didn't work, and the lights are still both on after checking the tray and moving it away from sun, there might be a deeper sensor fault. Your next step is customer service. Don't try to take it apart—the unit uses flammable refrigerant.