What identifies the immortals in the culture, in Part 3, Chapter 10, and what sorts of things must these immortals endure?

Gulliver explains that there are some in the culture that are born with a red birthmark over the left eye and that these people were immortal. When the child becomes older, the birthmark changes color. Even though they do not die, they do age and become frail and feeble. They also must watch their loved ones die.