In response to Carla Holley's comments about eyes on hats, I have been
divebombed by many species of nesting birds, some of which can clobber you
if they hit you, and, invariably, if I looked at them they didn't hit me
(you learn quickly not to turn your back on a jaeger or skua). Good
eyespots on a hat would probably deter them from hitting one from behind.

Pygmy-owls and kestrels have fairly effective rear eyespots, something that
makes sense for a smallish bird that perches in the open for long periods
and would be subject to predation (and mobbing, come to think of it) from
behind.

Dennis Paulson