Bushy, I have been reluctant to reply to your question in fear of being laughed down, but the short answer is no. There was no such thing as a HT equipment schedule and the HT did not come in a chest with all the bits and pieces as per the No.4T or later versions
The HT was not a "weapon system". Such terminology and practical reasoning came much later on within the ADF.
Battalions were allocated a list of stores which may have included telescoped rifles, either No.3T or HT, scout regt. telescopes etc. depending on the timeframe, the Bns operational role and availability of such niceties.
Pte. Bloggs and his spotter would simply rock up to the QM or CQMS and sign out whatever they needed or what was available at the time in order to get the job done. As they were in Admin Coy. and working directly under the Int. Officer, they were given a lot more leeway than a normal Digger when it came to controlled stores.
Generally, controlled items commonly drawn by HT users included a compass prismatic, scout regiment telescope, watch GS and binoculars prismatic no.2.
Obviously non controlled stores used would have been gridlined paper notebooks for making maps/scaled sketches, local maps etc.
Items for camouflage and concealment were made/procured by themselves.
Reallocation of Government property (not necessarily ours) for best use has long been a hallmark of the
Australian
soldier.
One has to remember that following WW1, the sniper was not seen as an "honourable" soldier by the general public and quite a few of their fellow soldiers. There was a stigma attached to the role, which is why the art was lost for so many years by the ADF and consequently there are limited first hand references to their activities.