It's interesting that the thread you posted implies that it was new in Series 3, but I found one above that was all the way back in Parting of The Ways, unless I'm mistaken. Now that I'm looking at it again, I think it might be a detail on all of the props (at least the early ones), and the one I posted that's missing that cover is actually just hidden behind the eye disks.

I believe it's a cover for a pulley and drive belt. Most likely bigger components than those used on the first prop.   There is some discussion about it here:  

I wanted to ask about this extra cover piece on the dome, to the side of the pivot. These images show what I'm talking about. The pivot under the cowl looks like it has some kind of cover next to it. I remember reading somewhere that there was a manually controlled dome that was sometimes used. Is that what this is? I can only find one or two pictures, and even other pictures of this specific member of the Cult of Skaro (I think it's Thay?) seems to be missing this cover piece.