I grew up in that neighborhood 60's-70's, still have family there.
There was no official name for the area, but our neighborhood baseball league was called the 'Redford Park Athletic Association', we always presumed the neighborhood name was Redford Park.
The Eye is a silly name for the neighborhood, but as you said, the neighborhood watch association is called 'The Eye' . That name referred to 'watching', nothing to do with the neighborhood name [[My Dad was one of the 'charter' members and remembers the naming choice at the 1st meeting.
Maybe some genius saw 'The Eye' signs and thought that was the neighborhood name, it has 'stuck' since.
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