The old waiter and the customer (the old man) both have known loneliness, despair and nostalgic melancholy. The old man drowns his sorrows to pacify and occupy his time and the old waiter focuses on his work. Unlike the young waiter, the customer and the old waiter have faced this loneliness, this void and have only one thing to keep them going: a clean well-lighted place. The old man gets solace from the cafe because of the welcoming, soft atmosphere. It is literally a quiet, peaceful light in the void: darkness/loneliness. The old waiter gets comfort in providing such a place for those who need it. He says he likes to stay late at the cafe for those who need the light. This is literal and figurative; the cafe is an actual sanctuary and when the customer leaves, he will remember the cafe as a symbol of sanctuary. So, they both find solace in the cafe; a sanctuary.
The difference is that the old man despairs, while the old waiter finds some comfort in knowing that many (i.e. the customer) must have insomnia. Here, insomnia literally means insomnia but it also refers to "many must be lonely," and the old waiter finds comfort in knowing he is not alone in feeling alone.