Rudi: Many, many thanks! Yes, this is the same parade baton that Ludwig appears to be holding in many photos, including a good one in the Jan Kube book of many years back.
Question: Do you recall if it was this pattern on all sides? I must assume so.
It is interesting that a photo of a military review in Germany interwar, of Princes Rupprecht and Leopold, show each holding Bavarian parade batons of different appearance. (Yes, I know they were both also Prussian field marshals but these batons are distinctly not the Prussian pattern). The batons they hold are not only different from the Ludwig III but also from each other! It may have been that Bavarian field marshals, particularly of the Royal House, were allowed a lattitude in the design of their own batons.
The top interimstab appears to be a Prussian one, which would be correct also as Ludwig III was made a Prussian field marshal.
The middle one is clearly the Bavarian interimstab.It is the only color photo I have ever seen, and has more detail than any photo I have yet seen.
I will treasure these photos as they are likely the only ones I will ever see, in color and close detail!