The third Arkentool is almost certainly the Satellite Dish atop Charlescomm, and the deeper reason why it works is because it is capable of recognizing/interacting with the waves in the Grandiocosmic Strings that govern the minds of Erflings.
The Arkentools in general will turn out to be indicative of the Earth Universe (as in they are all tools which are essential in the Earth Universe but are either non-existent or under-valued in the Erf Universe); they will also turn out to each primarily utilize one particular branch of Fate aligned magic (Thinkamancy and Croakamancy are both Fate and the Changeamancy that the Hammer seems to utilize is also Fate).
If the Arkentools are indeed "Tools of Fate," then I suspect that either Flower Power or Findamancy (Changemancy is elementally matter, and Croakamancy is elementally matter and motion; Thinkamancy is elementally Life and Motion) as both Motion and Matter are currently well represented amongst the tools.
Since the Tools seem to be indicative of the Earth world we might very well see an Arkentractor or Arkenscope.
To bring you up to speed.
We have been told in the comic that there are 4 Known Arkentools. (Parson's Stupidmeal in Book 1
). We have encountered 3 of the 4. The Arkenhammer, the basis of Stanley the Tool's name, the Arkendish, the basis of Charlie's entire empire, and the Arkenpliers, wielded first by the living Ansom, then by Wanda.
The comic states that the Magic Kingdom has theorized that the Arkenpliers extend Croakamancy into the Element of Life as well, thus allowing Decryption instead of simply Uncroaking. There has been forum speculation that the Arkendish extends Thinkamancy to the Element of Matter, although my personal opinion is that it simply amplifies the abilities. There is no definitive statement on how the Arkenhammer works, though the most common theory is Stagemancy.
We have been explicitly told there is a 4th Known Arkentool. Stanley said that it was common knowledge. Yet the comic has never mentioned a single word about it besides two panels in one strip. Speculation has been abundant about what it is. The two most common appear to be Dirtamancy (for Sizemore) or some form of Hippiemancy (the most popular theory recently seems to favor Signamancy).
"All warfare is based on deception" - Sun Tzu, Chapter 1, Line 18, The Art of War
"The principle of strategy is to know ten thousand things by having one thing." - Miyamoto Musashi, The Book of Earth, Go Rin No Sho