Common names can be confusing, with similar or identical names applied to different species. What I think you're referring to as redeye (or Coosa bass- M. coosae) look a little bit like a smallmouth, a little bit like a spotted bass. They're native to SC as well as AL, GA, parts of TN and NC, and they've been stocked in a few southeastern streams outside they're native range, ostensibly because they can persist in smaller creeks than the native smallmouh. I've only fished for them in Tennessee, and few exceeded twelve inches- not tackle busting smallmouth, but a neat fish that lives in some awfully pretty streams.
Like smallmouth they tend to hang out in moving water near boulders, logs, and patches of emergent aquatic vegetation. They tend to eat aquatic bugs and crayfish, maybe the occasional small fish. The ones I found weren't picky- buggers, leeches, and sparkleminnows all worked well. They weren't shy about taking anything off the top, either- large sponge spiders, small Gurgler-type flies, small deer-hair sliders or cork-bodied Sneaky Petes, and those light blue Shenandoah Popper patterns (don't know how else to describe it, but googling "Shenandoah Smallmouth Popper will get you images) all worked well.