I thought that the idea of Zen is that I eat when I am hungry, I drink when I am thirsty, and I sleep when I am tired.
That sure sounds like Zen. But it can also be described as an even more fundamental attitude of being in the moment, without an ambition leading you astray, as in the concept of sit to sit, but not to reach this or that. Eat to eat, drink to drink, et cetera. Of course, any action contains its own reasons and effects, but they are often accomplished the best by our minds not focusing on them.