When I first saw it I also thought of a conductor's baton, but on reflection, I'm not so sure. It looks a little too 'ornate' and it's shaped almost as if to be gripped in the hand (middle section in photo 2 which seems to be about 4", just right for the size of a hand ... as any horsey person out there will recognise ). So I'm thinking that perhaps it was a swagger stick, which might also account for it's decoration. I doubt very much whether it would have started off in life as a teaching stick, a little too fancy, but who knows what it was ever used as?
Just read the description again, and am wondering about the 'brass rings'. Are you sure they are brass, only that if this was a quality piece then it would be more common for any metalwork top be at least silver.
Also, have you tried using it as a 'conductor's baton', given it a few waves holding it as a conductor might? I have a feeling that it might be too weighty and not balanced, but not based on anything other than those two small pics.