You are correct, Tim. But "red eye bass" is another colloquial name for Rock Bass or Warmouth ... unless you're in Texas. That's where the true Red Eye Bass lives ... or at least, that's where I've caught them. Mostly in the streams near Houston. First one I caught really took me by surprise, because the eyes were bright red.
That's not mine, but it's exactly what I caught. I'd never seen a bass with red eyes before.