It is indeed, the order, eyes right, is made and the salute is both given and received, I certainly cannot comment on the goat, other than to note a similar appointment, to the rank of Lance Corporal, but, in the particular case of Lance Corporal Cruachan, his medals and rank are clearly visible, on parade, his mane is brushed to the right of his neck from poll to withers.
Regarding entitlement, the difference between Troop Horse D36, Freddy and Lance Corporal Cruachan, is simply that the former actually went to South Africa, fought and earned his medal and clasps with his Squadron, the latter, whilst merely a mascot, actually was in the paid service of his regiment and he was appointed to his particular rank.
He wears the medals, to represent the service of his regiment, so those particular medals that had been earned by his regiment, during the period in which he actually served with the regiment, his replacement will have to go onward and receive entitlement to any medals subsequently earned by the regiment, he has two already!
I will assume they would be officially named, perhaps a letter to their RHQ, would confirm that, his replacement, certainly his a lot to live up to, but, I have no possible doubt whatsoever, the extremely high standards with be maintained.
SWB wrote: I suspect it has something to do with enabling the medals to be seen on parade, is the animal's rein always held in the right hand?