reflectors, reflected light, light

I found a rear bike reflector the other day by the side of the road. I find reflectors often. They seem to jostle loose. I zip-tied it to the back of my helmet. Why not? When I was a kid (even into my early thirties) I'd take off every reflector I could thinking they were uncool. Now I've got them just about everywhere. Still there seems to be a blind spot in front of me to the sides. Cross traffic at night (especially on dark roads) doesn't seem to see me well enough. Which maybe is okay because I see them and I slow down but I want it to be better/safer than that. Reflectors only light up when there's light shining on them. And cross traffic lights aren't facing the right direction. And bike lights, even the strong ones, don't provide much lateral light that a car driver might see. A glowing helmet would be interesting. At least, a white helmet probably helps. I'm considering a helmet mounted light.