Found the issue but not exactly understanding why.
The Camera has a Rigidbody component, because I wanted it be be carried around by other moving objects. Changing the flag to 'Is Kinematic' to TRUE makes all the MOUSE DOWN events happy and lively.
Quote the manual: "If enabled, the object will not be driven by the physics engine, and can only be manipulated by its Transform. This is useful for moving platforms...". I need to read up more on what this is about.