Eyelid myoclonia with absences and eye closure induced seizures is characteristic of:

Eyelid myoclonia with absences and eye closure induced seizures is a hallmark of Jeavons syndrome. This condition is characterized by brief episodes of unresponsiveness (absence seizures) that are often triggered by blinking or eye closure. In addition to these absences, individuals with Jeavons syndrome also experience myoclonic jerks, particularly involving the eyelids. The unique aspect of eyelid myoclonia differentiates it from other syndromes.

In contrast, Ramsay-Hunt syndrome is primarily associated with herpes zoster infection affecting the facial nerve and does not typically present with eyelid myoclonia or absence seizures. Rasmussen syndrome involves progressive brain damage and is characterized by seizures but not specifically eyelid myoclonia or absences. Landau-Kleffner syndrome is related to acquired aphasia and seizures, but it does not display the specific feature of eyelid myoclonia associated with Jeavons syndrome. Thus, the characteristics of Jeavons syndrome make it the most appropriate choice given the symptoms described.