Following my recent post on Horse Holders there was a note that Horse Artillery would have similar needs.
I found a mention of Horse Artillery, Horse Holders, in the 1864 version of Instruction for Field Artillery, which was used by both sides. The 1860 edition being the standard at the start of the War.
Officially, each Horse Artillery piece was allocated two extra men whose specific job it was to hold the horses of the gun crew behind the line of Caissons.
The book doesn't go into such specific detail as the 1862 Cavalry equivalent as to the holding of the horses but does say who is supposed to hand or receive (when mounting). Left hand gun numbers to the left hand of the holder and right hand one to his right.
Both the mounted holder and dismounted holder options seem unsatisfactory here. The mounted leaves me wondering about the control of the holders own horse and the dismounted gives a vison of the holder being dragged off in two directions at once!
As the mounted arm had its own established practice I'm going for the Horse Artillery following their ideas. With the two mounted men controlling the horses from the saddle.