Okay, I'm confused. Late evening/night flights aren't necessarily red-eye flights.
Westbound flights, and continental-US north- and southbound flights, are rarely red-eyes. They may depart in the evening, even late in the evening, but - due to the relative lack of distance north and south, and due to the time change from east to west - they're just plane late evening flights.
Red-eye flights are flights such as the ones specified by CarolA - they leave the west coast (or close) airport late evening/night, fly all night due to the time change, and arrive at the east coast destination airport generally at or after sunrise the next day - or, as in CarolA's case, many hours later the same day.
They're nicknamed 'red-eye' because you fly when you'd ordinarily be sleeping and so even if you're lucky enough to doze for a while during the flight, it's not a GOOD sleep - so you disembark with, well, red, tired (Visine-seeking) eyes!