Something like a knee-jerk reflex doesn’t involve the brain at all and could persist. The reflex that is usually checked is pupil dilation which involves midbrain circuits. Tracking someone with your gaze uses both midbrain and cortical circuits.
Docosc or another medical professional would know better, but my understanding is that peripheral reflexes alone would not prevent declaring a patient dead, but anything involving the brain like pupillary reflexes would.
