I recently purchased a Spaulding & Co. French made visible Brocot mantle clock. The case is wonderful but there are 2 pieces missing on the right upper side, as where the soffit is on a house. Looks like the "glue" did not hold for all these years.
Is the material available or the parts available
You would have to have the missing piece custom made by someone who works with marble. Hardest part is finding a matching piece of marble to cut it from. Not a common case where you might find a donor.
I use either a local monumental mason or a company in Italy to produce missing and damaged pieces, depending on whether the local mason can find the type of marble I need.
In your case I think it will be difficult to find a matching stone. I am not an expert in exotic marble types but can suggest you look at Breccia Pernice, Rosso Magnaboschi and Rosso Sicilia as possible candidates.
Having looked at your photos again I think your case may possibly have been made from a French marble. These are not as well known as the Italian stone types but red marbles were (are?) produced in Languedoc and other regions. One very red variant was called Rouge Royal. It had these light gray details.