whoa wait...red eye in video? I don't believe I've ever seen that. Anyone else ever seen something like that?
As far as I know, it's a still camera problem. Happens when a flash goes off and bounces off the retina because the iris of the subject's eye is wide open (dilated). The reflection of the light causes a red spot in the eye.
So, I'm not sure how you're getting red eye in video. If the light is on constantly, the subject's eye would automatically adjust accordingly; thus, no red eye.
Can you post a screenshot of what you're talking about?