Here are 2 ideas based on the same principle: create holes in an Icosphere, put a Point light inside and surround it with a Volumetric Scatter cube (density 0.04).
The first idea creates "transparent" holes using a voronoi texture node setup and uses the "Is Camera Ray?" Light path node to hide the holes to the camera. Quite versatile as it can be used on ...
This feature is known as Light Linking, and it doesn't exist in Blender as of 2.81a
There is a todo item to include this in the future: https://developer.blender.org/T68915
What you can do is render in multiple view layers with only certain objects and lights together in a layer. Create multiple view layers, and enable/disable collections to include them ...
That happens when you have hidden "layers" in an old version of Blender and open it with 2.8x. To show the items click the tv and camera-icons to make everything visible again.
See the second image, click the tv-screen and everything is visible again.
I provided a video for better clarification, also used Eevee because the render is fast, but you can use cycles too.
What you want is to simply animate a emission property and a light brightness, in the case of cycles, you could use only the emission shader.
You will also need another shader when the light fades off, so you mix the emission with the other ...
Use the Light Path node to make the material appearance different from its influence.
From Add > Input > Light Path use the Is Camera socket to mix between your Emission Shader and a Transparent Shader.
The reason you are having problems is because you added a Mesh Circle instead of a Curve, Circle. Look more closely at the video 20:05, where he Add > Curve > Circle
Thats not the same as a Add > Mesh > Circle !
See screenshot below :
In the Outliner it should say BezierCircle :)