Phineas Gage is a terrible example: he suffered incredible frontal lobe injuries. Neuroanatomy is much more complex than "part A performs job X", but the frontal lobe is particularly important in executive functions. More caudal structures are more closely associated with emotion, in general.
Damasio bases his conclusions on his own patients, not Phineas Gage, who is provided as a famous example for historical context. The only reason I'm mentioning only him by name is I remember his name and I do not remember the names of Damasio's patients. I actually think he doesn't even give their real names since they're patients and subject to confidentiality laws.