Why is my light doing this when it's being recorded?
I filmed it with a Nikon D3000, it didn't do this to any of the other lights I was filming that were similar.
Looks like a Strobe Effect as the light flashes on and off with the AC current. (To fast for the eye to see but the refresh rate of your camera catches it.)
It is the frequency of the light - it does not glow steadily from a continuing source of power, but is powered in pulses.
Another instance of this phenomenon may be observed if you stretch a rubber band in front of a tv screen/pc monitor and strum it - the refresh rate of the screen will enable you to see a stroboscopic effect and the rubber band appears to have a waveform travelling along it in slow motion.
It actually looks like you filmed a light, played the video of the light on a TV or monitor, and then re-filmed the TV/monitor image.