Hi Ian,
Camping atop Giles is permitted, and is awesome, although occasionally it's too windy to camp up there. There are suitable spots for three tents plus a couple of bivy bags. You are supposed to pay $4 per night and book in advance:
https://nt.gov.au/__data/assets/pdf_fil ... -sheet.pdfThat PDF file includes a map, about which I have a few comments. The route they mark goes through quite a lot of spinifex and you may prefer to go along the east branch of Ormiston Creek instead, as far as the spot that they name "Camp 1" before rejoining their route. You can ignore their "Camp 1", since it's not particularly special and you can get closer to the base of Mt Giles on Day 1. On Day 2 you climb Mt Giles (up and down) and continue east to Giles Yard Spring. A lot of prickly wattle has sprung up at the top of the creek, but if you fight through it you'll find plentiful and beautiful water trickling down a waterfall. In a wet year there can be water flowing lower down but it is sometimes soiled by cattle. On a longish Day 3 you would head out to Inarlanga Pass and rejoin the Larapinta to Serpentine Chalet Dam.
There is good camping in the creekbed near the "M" of "Mt Giles Campground 2" and the water upstream is fairly reliable. You can also find some suitable spots to camp closer to the base of the ascent. The ascent route marked on the map is the best one, and there is usually water at a small seep 100m up the gully to the west of that ascent. Giles Yard Spring has excellent water which is considered to be permanent. This year you will probably come across other water sources, but these are the more dependable ones.
To camp on the summit it's best to take 4 days from Ormiston Gorge to Serpentine Chalet Dam, or else you have a very solid Day 1 and end up climbing Mt Giles in the heat of the afternoon.