So, in answer to your question about what "Sigs" stands for, Yes, it is military shorthand for Signals used at that time.

The officially stated role of the Royal Australian Corps of Signals has, unsurprisingly, changed over time as technology has evolved, but the role is one that facilitates communications between units at all levels.

Signals units were required to man communications stations (either fixed or in some cases portable), deploy, maintain and recover communications equipment, provide for the encoding and decoding of messages.

In the combat conditions experienced during the Kokoda Campaign, this was a lot harder than it might sound - as you can imagine weather, mud, exceptionally difficult closed terrain and enemy action took a consistently heavy toll on communications capability during the campaign. As much as the conditions there were horrible for anyone, your Grandfather would've unfortunately been no exception to those conditions.

Whilst Peter FitzSimons' book on Kokoda is popular (He's a writer/columnist/journalist... not a historian), and an easy and occasionally entertaining read, it's far from an academic work and does suffer from occasional errata, personal bias and a healthy dose of what our serious historians refer to as "Anzackery" - exaggeration of both the significance and quality of Australia's military record fueled by parochialism. By all means, continue with the read, but once you're done poke into other sources as well - The Australian War Memorial has a wealth of resources online for you to delve into.

As an example, from the Official History, Volume V – South–West Pacific Area – First Year: Kokoda to Wau (1st edition, 1959) can be accessed here, and I'd suggest taking his unit (Since you've obtained his service history details, persumably from the National Archives of Australia) and matching it up to either broader Official Histories or browsing the AWM site for an Official Unit History or a Regimental Diary - these more granular sources will provide a better chance of you being able to match places, times and your Grandfather, although bear in mind that unit diaries can be in and of themselves quite high level, and will generally only refer to very low level subunits and individuals either because such a subunit or individual does something exceptional, or is caught up in a detrimental event (and even in the latter, Officers are far more likely to be mentioned by name e.g. "Section moved to 1 Company position, ambushed on way. Lt J Browning KIA, along with 4 O/R's" (meaning 'Other Ranks' - enlisted soldiers).

Also, don't be afraid to contact the AWM directly if you have trouble tracking down an individual unit using AWM online resources. They may not have time/resources to help you with individual queries about your Grandfather, but they should be able to help you decipher acronyms and terms from his service history that you can't, and should be able to help you identify and place certain units at certain times, or at the very least show you where you can find that information yourself.