Forgive the question from an amateur, but would a point red light be corrected bythe camera's red-eye reduction if selected?
Red-eye reduction is a function of using the flash. A pre-flash is fired before the shutter is activated, with the intention of causing the iris to close and ameliorate reflection of the main flash from the retina. I don't think it'll make any difference to photographing red points of light.
I just did a quick test of my Canon PowerShot G9, and it struggles with any point of light, because the intensity is such it can't be exposed accurately compared to the surrounding scene. The subjects in this case were the power LEDs on my computer monitor (red) and PC speakers (green). Both were washed out, but the red was distinctly orange at the centre, fading to red in the outer glow.
My phone (and elderly Nokia N73 with a 3.1MP camera, showed the same issues. Even obliquely, the pinpoints were overexposed, the centre area orange, and the outer area showing red.
I don't know how to overcome this, apart from lowering the intensity of the LED so it's barely showing. *shrug*