To clarify, there are three characters in the story, two of whom are older than the young waiter. Hemingway's "old man" is a deaf patron of the cafe who stays late to drink alone on the terrace. The young waiter, wanting to close and go home early, resents his presence and treats him rudely. The other waiter, however, is an older man himself, developed in contrast to the young waiter.
The reader logically might expect the older waiter to demonstrate more understanding simply because he has lived longer and experienced more of life; this inference would be correct. The older waiter is far more understanding and empathetic than is the younger man. The young waiter shows his ignorance of life and human experience early in the story when he talks about the old man's recent suicide attempt, saying the old man had no reason to despair because "[h]e has plenty of money."
The older waiter lacks the young man's brash confidence; he knows life better:
I am of those who like to stay late at the cafe . . . With all those who do not want to go to bed. With all those who need a light for the night . . . Each night I am reluctant to close up because there may be some one who needs the cafe.
When the older waiter does leave work, he does not go home. He goes to another bar, not as nice as a cafe, but a place of light, as well. Eventually, he must leave even this place:
Now, without thinking further, he would go home to his room. He would lie in the bed and finally, with daylight, he would go to sleep. After all, he said to himself, it is probably only insomnia. Many must have it.
Unlike the young waiter, the older man understands personal loneliness and the ultimate spiritual loneliness that comes from the belief in "nada": "It was a nothing that he knew too well. It was all a nothing and a man was nothing too."