Hi Mike,
Light sources have by default no shadow. What you see (not having your scene file here) might be exactly this.
There are three different ways to create shadows with the C4D lights, Soft-Shadow Maps, Ray-trace (Hard) and Area.
Besides that, your scene has one light source set to Ambient Light, if I take the scene file from the previous question. Ambient Light is a light source that adds just light everywhere. It might not show up clearly when Shadows are enabled, but it is kind of a weird set up to have both. Ambient light was used in the early days to provide a minimal light distribution to a complete scene, or if set to negative to subtract light. If the light had a color, then the complementary color was left. Today this is mostly replaced by global Illumination.
As a side note, shadows can have a certain Shadow>Density. If not set to 100% such artifacts might happen, as the light continues to move through the scene. To set the color of the shadow to anything but black will allow for similar (unwanted?) results.
Let me know if this scene is the scene you mentioned earlier, I can be more precise.
All the best