The Spanish word draws on a part of a house and listening in by association. The eaves are a part of the house in English and an eavesdropper listens in conversations because they are nosey.
Associating the nosey neighbor with an external part of the house is universal. Consider the Chinese word for [eavesdropping|http://en.bab.la/dictionary/english-chinese/eavesdropping]eavesdropping and a native speaker would see an ear next to a gate.