There is indeed more to say about the gnomon.

Gnomon means literally a thing enabling something to be known, observed or verified.  Well before Euclid, it was the term given to the vertical pin in a sundial placed to measure time by shadows thrown by the sun; the word signified the placing of a staff perpendicular to the horizon. But in more ancient times it was considered that the connection between the gnomon and the square to which it is added was symbolic of union and agreement. So the philosopher Philolaus (c. 460 BC.) used the idea to describe knowledge, making the knowing embrace and grasp the known as the gnomon does the square. 

Think about the boy looking at the window, looking for it to be illuminated by the yellow candle light, waiting for something to be known.  A little imagination and you can see him standing there, vertical as the sundial pin.  Only it is night.  In the early 1900's the street would have been lit by electric lamps. And perhaps would cast a shadow. Above him, the window is a lighted square.  He is the shadowy gnomon. He needs to grasp knowledge, to understand, to be complete, himself. 

Regardless of how you visualize the scene, this is what this story is about.