If you look ever so closely at the cap badges that are apparent, (including that on the B&W photo of Private Elphick),the belt buckles, and the badge of rank on the Sergeant Major, they are all similar to that of the Grenadier Guards, although on the Headstones of the fallen they are commemorated with the older badge of I think a dragon speared by a lance or something similar. This is because during the First World War, I believe, they were affiliated to the Grenadier Guards and fought as Infantry (at least 2 Battalions IIRC). Similarly, their No 1 Dress Forage Caps are styled in the same fashion as the Grenadier Guards Forage Caps, but with the addition of a single thin black band running through the centre of the scarlet band.
Their Artillery role was purely ceremonial during the Cold War although they trained for the same kind of surveillance and patrol operations on behalf of Comd Arty Div, 1 (BR) Corps, as those carried out by 21 and 23 SAS (V) Regiments (ie: CPU).
The badge on the headstones is the 'short arms' crest, basically the top of the regimental coat of arms.
This is worn on the berets of all HAC soldiers with the exception of the Corps of Drums who wear a Gren Guards style grenade with a Household Div TRF backing. The grenade is in silver instead of the Gren Guard's gold, it also has HAC on the ball of the grenade.
This grenade badge is also worn on forage caps when in number 1 dress (artillery or infantry blues). SNCO's have the same badge but HAC is in gold lettering. Officers have a smaller embroidered badge.
Now it gets even more confusing.
HAC officers while carrying out gun salutes and artillery ceremonial duties in number 1 dress will wear a Royal Artillery cap badge but with the HAC motto instead of the RA one.
Collar dogs are not worn on infantry blues, they are however worn on artillery blues in the form of a small metal grenade.