HI Blake, Cool lamp!
That might have to do with the Radius of your Light (and what sort of Light you are using). Part, might also be coming from Indirect Light, as you can see in this small example:

In your case, it looks like you are using a Point Light and reducing the Radius will give you a harder Fallof, so maybe use a Spot Light. That doesn’t shine in all directions.
More advanced, would be to use IES Lights, but that seems a bit overkill in a situation like this.
Or even using Light Linking, by making the ‘bend’ a separate Object and exclude it from being lit by that Light.