One of the things we learn about the astrologer in Narayan's story is that he's not quite what he seems. Later on in the story, for instance, we will discover that, back in the day, he brutally attacked a man and left him for dead.

Long before then, we learn that some of his clients, his simple clients, ordinary, ill-educated folk, don't know who he really is. They mistake the astrologer for some kind of prophet. This adds to the sense that the astrologer is not the man he seems to be.

They arrive at this false conclusion from the "sharp, abnormal gleam" with which his eyes sparkle. Just one look at those eyes is enough to convince the astrologer's clients that he is a true prophet. This makes them feel comfortable and explains why so many of them are prepared to become the astrologer's clients.

In actual fact, however, there's a much more mundane explanation as to the sparkle in the astrologer's eyes. Far from its being a sign of his prophetic, mystical powers, it is in fact an expression of his continued search for potential customers. The undeniable power of his eyes is enhanced by their position between his painted forehead and dark whiskers. His eyes are clearly a unique selling point and help the astrologer drum up business.