你误读了句子结构。being在此为名词。

《韦氏高阶》being 不可数名词

[noncount] formal : the most important or basic part of a person's mind or self

• I knew it was true in the core of my being.

• He loved music with his whole being. [=he deeply loved music]

所以你应该知道这个句子三个分句都是一般过去时谓语：

My mouth watered for it, my stomach craved it, my whole being begged for it. 

你会注意到，前二个分句主语为my mouth, my stomach, 可能还有my heart, my eyes等未提及，即列举是不完整的，所以这二个分句不用and. 而第三个分句主语my whole being （我整个人）则是对我身体部位的总结，与前二个分句不是同一个层次，而是对前二个分句的解释、补充，不是并列关系，不能用and。结果就导致了逗号句。这类似于：

Tom likes it, John hates it, everybody has a different opinion on it.