The older waiter says to the younger, "we are of two different kinds," this establishes the most obvious conflict. The younger waiter is more selfish, 'in a hurry,' and the older waiter is more selfless: inclined to stay at the cafe in case someone (like the old man) needs it.
The old man needs the light in the cafe and the old waiter needs the daylight before he can sleep. 2) The younger waiter doesn't need to stay, he seemingly has everything: a waiting wife, a job, and he even says that an hour means more to him than it does to the old man. This seems logical given that the old man recently tried to kill himself, but it is not. The younger waiter has no way of knowing how much that hour at the cafe means to the old man. But the older waiter does know how much it means.
At one point, the younger waiter tells the old man, he should have killed himself. He says this knowing the old man is deaf, so it is an empty statement, a meaningless effort. But the young waiter really believes that an hour to him is worth more than the old man's life. The most simplisticconflict is between selfishness and selflessness. But the deeper conflict is between light and dark. One interpretation of this conflict: The younger waiter is in such a hurry that he never stops to think; he'd be more inclined to ponder things more deeply. Full of confidence, he's convinced that he has everything. The older waiter makes a joke that were he to go home early, he may find his wife gone, or with another man (these are just intimations; its open to interpretation). Being in such a hurry, the younger waiter may be too scared to stop and think about what he may not have, or what he may lose (eventually he will be in the position of the old man - if he outlives his wife and retires).
The conflict goes deeper here. The old man is in despair, he is facing the 'nada' of his existence, so he is in the dark. He needs the clean, well-lighted place because it gives him a sense of order, quiet, peace. The older waiter recognizes this (and the old man may in fact know the older waiter sympathizes); therefore, there is a solidarity. Solidarity is something the younger waiter also lacks. Since he lacks solidarity, he is alone (sole) and more in the darkness than he thinks: he can't contemplate this because he's always in a hurry.
In the end, younger goes home to his wife, older goes home to insomnia until first light. The old man wanders off. Clean/unpolished, Light/Dark, Solidarity/Selfishness. The old man and older waiter get as much (or more) meaning out of the peace and solidarity of that extra hour than the younger waiter gets with his hurrying. They get this because they have a sense of existence that is greater than themselves. The younger waiter is concerned only with himself, and will miss out on some things as he 'hurries' into old age.
Its an internal conflict an individual has to face when confronted with the 'reality' of his existence. Its more or less perception driven, but every individual at some point of time struggles to hold his existence in dignity when he realises the futility of an exercise called 'living'.
--i hope this line would help you in your analysis. All the best!