The reason the red light appears white in the picture is that it is significantly overexposed. Even the small amounts of blue and green in the red light are enough to saturate your sensor in red and green, and almost saturate it in blue. Thus it appears almost white. Look at it this way, if your camera reaches saturation at a value of 255 and there is enough red in the light to reach 2500, enough green to reach 1000, and enough blue to reach 400 then all three channels will be totally saturated (255, 255, 255), even though there is more red than green or blue in the actual light.
To get the color of the red light to show accurately in your photo, you must reduce exposure until none of the color channels on your sensor are totally saturated by the light. Of course this will create problems with the rest of the scene which will be much darker. You will either need to illuminate the rest of the scene to raise it closer to the value of the red light or do as others have advised and combine two exposures: one properly exposed for the red light and another exposed for the rest of the scene.