Step 1: Frey's syndrome (auriculotemporal syndrome, also called Baillarger or Dupuy syndrome) is a complication that typically follows parotid gland surgery or injury near the parotid region.
Step 2: It results from damage to the auriculotemporal nerve, which carries parasympathetic secretomotor fibres to the parotid gland and sympathetic fibres to the overlying facial skin sweat glands.
Step 3: During healing, the regenerating parasympathetic fibres aberrantly connect to the sweat glands and cutaneous vessels. As a result, eating triggers facial sweating and flushing instead of salivation - the classic gustatory sweating.
Step 4: Hence the injured nerve is the auriculotemporal nerve, option (a). The great auricular, lingual and inferior alveolar nerves are not responsible for this misdirected gustatory sweating.