I have not seen a light with such a hole in the middle but there might be something that works. I know that you can get light guide wires, an optical fiber attached to a lens cap. That might work if you attach the output end of the wire onto the probe to provide light.
How small and how bright does the light have to be? You might be able to attach a 1 AAA light to the probe if there is enough space.
:welcome: