To display dynamic lights, X-Plane 11 requires HDR rendering. If HDR rendering is disabled, for example, switch lights are displayed, but landing lights and other cockpit lights are not visible. To solve this problem, simply enable HDR rendering again.
To do this, simply go to the Settings → Graphic Settings and move the Visual Effects slider to the right until HDR is in the brackets. This is the case for the last two points High and Maximum.