It is the no shadow at midday on the summer solstice if you are on the Tropic of Capricorn that has me.
To form no shadow, light has to travel vertically down. We can try this with any light source we want. Like I demonstrated the other day, you can't have this as a single reflection on any shape if the light source is at the same level as what you are shining it on.
But this could work with a pair of triangular prisms, perhaps that is what is going on. If you took a flat surface and placed a light source shining straight up, then placed a right angle glass prism at some height above, then you could turn the light 90 degrees and have it travel horizontally. You then need another prism to turn the light 90 degrees again and point straight down.
To modify the dome so it works, all you need is a floating prism which rotates fully over the course of 24 hours, placed pretty high above projection central. You then have another prism (which could be attached to the dome or floating) above the tropics, directing the light straight back down. That secondary prism would drift over the course of 12 months between being over the Tropic of Cancer and back to the Tropic of Capricorn. It would also travel around the globe every 24 hours to maintain aligned with the central prism.
I've said all the long that you can't build a working model of the flat/dome earth where you can for a globe, but actually the addition of two prisms to change the reflection angle and it works quite nicely while both explaining shadows and seasons.
Does this sound like a reasonable mod?