Reverence is a deep respect shown to someone or something.
Usually, when you revere something, you know why you do so, and it is colored by that knowledge. One reveres a mountain for its majesty, or a perfect rose for its beauty.
In this case, Smith does not really understand why it is singing, but he knows it's not for a specific audience. This is particularly sharp because his own life is, and he knows it is, under constant surveillance, making just about everything he does being for the watcher. He does not articulate this difference (perhaps he can't bring himself to?), but the result is that his reverence is therefore vague -- he does not know exactly why he reveres it.