I reckon the guy will go bush, and won’t be found for weeks. And it’s a toss up if he will be even more mentally disturbed when he is found or will have calmed down a bit. Searching for him on foot or horseback with or without dogs is bloody dangerous if he’s armed and apparently he is. And the local people/cops know this and will be keeping a very beady eye on isolated sheds and eatable livestock in distant paddocks. Never underestimate the bushcraft of nutters like this one cos they are sometimes quite impressively skilled in survival stuff. If it was me, I’d consider calling in a helicopter/drone and using thermal imaging to find him. Then the hard part would become actually catching him without getting shot.