...want it to look professional and not draw the eye, like turrets under eaves.
That's usually my goal also. Walking around my neighborhood I see a number of cameras under the eaves. Those in a contrasting color to the house stand out, but if they match the house color you have to look carefully to see them, at least from the sidewalk.
A year ago I posted some video from a vandalism incident to nextdoor, and several neighbors asked me where my cameras were because they didn't notice any. I had four outdoors in plain sight under the eaves. Just fairly small and painted to match the house. Only one was kind of sneaky, a bare board cam 25mm square, protected only by several coats of outdoor latex paint, color matching the rough stone it's glued flush against. Most people miss that one even standing right underneath it. Probably won't last forever but it's still working after one year+ outdoors.