A 38-year-old woman from Mumbai presents with a 3-day history of right ear pain, followed by facial weakness. On examination, she has right-sided facial paralysis with loss of taste on the anterior two-thirds of the tongue on the right side. Otoscopy reveals vesicles in the external auditory canal. Audiometry shows mild high-frequency sensorineural hearing loss on the right. Which nerve branch is responsible for the taste loss, and at what anatomical point does it branch from the main facial nerve trunk?