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how could a spotlight/searchlight or other illumination from an aircraft produce the moving rectilinear effect observed ...
One possibility - described by eburacum in post #22 above - is that the visible rectangle was only a portion of a broader light (beam; whatever) truncated by the cloud / haze mass that reflected or perhaps refracted it.
Another possibility is that the rectangle was more distant than the aircraft and represented a bright light or illumination from within the moving aircraft whose external projection was bounded into rectangular form by a window (or open side door on a helicopter) on the far (unseen) side of the aircraft.