Let us remember that the narrator has 1369 light bulbs in his illegal basement flat, which is clearly excessive. No human needs that many light bulbs, so we need to consider why the narrator feels he wants this many light bulbs and what he is hoping to achieve. If we think about it, it becomes clear that the answer to this question relates to the way that he feels he is invisible to society. In a sense, he is exploiting the fact that he can still impact the world that deliberately chooses to ignore him. The advantage for him is that he can do this without being forced to suffer the consequences a "visible" man would have to face. Just as the narrator never declares his identity in the novel so that he can speak freely, so he uses his invisibility to take electricity from the power company, exploiting the loophole of his existence, as they are forced to recognise that there is a drain on their power but, because he is "invisible," they are not able to identify where that drain comes from. There is therefore a strange ambiguity in this action: he simultaneously announces his presence whilst also hiding himself from those he wishes to attract the attention of.
There is also a second meaning to the huge number of light bulbs. We use light to see, and this is a novel about a man who tries to define his own identity free from the restrictions of society and the way in which they would fix his identity for him. Therefore, the light could be seen as a metaphor of the narrator trying to go through a process of seeing himself and working out who he is.