My understanding is that yes, the post would be held by a senior Sgt/Sjt who would be held in high regard, equivalent to a Warrant Officer by today's roles.
He'd also oversee the rough riders typically as well.
Agreed that in the era that we are discussing, this was a post for a commissioned officer, not an NCO.
Also no dispute that the riding master would be the holder of a regular commission (a lieutenancy, in the examples that I can think of) and would serve at the depot rather than as a troop officer, but I base my caveat on the fact that the cases that I have come across in British cavalry regiments were all men who had come up from the ranks. No doubt there are exceptions to to this; I am not suggesting that it was a hard and fast rule.
This is most certainly not to suggest that such men were not held in high regard though. In the 12th Light Dragoons, which I have studied and written about at length, the riding master was a protege of the regimental colonel who actively sought to advance his career and employed him in a number of extra roles not directly connected to his official duties but where trust and judgement were required.
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My understanding is that yes, the post would be held by a senior Sgt/Sjt who would be held in high regard, equivalent to a Warrant Officer by today's roles.
He'd also oversee the rough riders typically as well.