A nesting sea turtle looks like it is crying. What is the useful job?

Answer: Eye-side desalting

Cooling tired muscles — Cooling tired muscles fits the hot beach, but it misses the chemistry. The secretion is not mainly a sweat substitute. A cooling liquid would not need to be saltier than seawater; that detail points to export of excess ions, not temperature control.

Washing beach sand — Washing beach sand feels plausible because the fluid appears near the eye. But sea turtles make salty secretions because feeding and living at sea load them with salt. The eye location is an exit route, not the main purpose; the gland is doing body chemistry.

Eye-side desalting ✓ — Eye-side desalting is the useful job. Sea turtles ingest seawater while feeding, then large glands near the eyes release salt in fluid more concentrated than seawater. What looks emotional is a survival mechanism for keeping internal salt lower than the ocean.