The closing line of chapter twelve is a choice between two organs: the sage goes by the belly and not by the eye, and lets the one go in favour of the other.
The pairing is precise and easy to misread as asceticism. The belly is not being recommended as a virtue and the eye is not being condemned as a vice. A belly wants a definite and limited thing, is satisfied by it, and then stops wanting. An eye wants whatever it can see, is not satisfied by acquiring any of it, and generates further wanting from the acquisition. One appetite has a natural terminus and the other does not.
Read that way the line is not about restraining desire but about which desires can be met. The book is consistently suspicious of wanting that cannot be finished, and consistently untroubled by ordinary need: chapter three fills bellies while emptying minds, chapter eighty wants people to find their food sweet and their clothes fine, and chapter forty-six defines the calamity as not knowing what is enough rather than as having anything.
That distinction separates this book from the ascetic traditions it is often filed alongside. Nothing here recommends going without. What is recommended is preferring the kind of want that can be satisfied, and the reason given is practical rather than moral.