In Ancient Greek mythology an Argus was an alert and watchful guardian. Based upon the name of the organization and the birthdate you provide for your ancestor, it would be my guess that he belonged to a post-war local militia unit. Funded by the state, they proliferated Missouri after the war, and were initially used to maintain law and order in the chaotic conditons that continued to prevail. By the close of the nineteenth century I imagine the militias evolved to be more of a social club than anything else.
I would also note that nineteenth century newspapers commonly were named Argus, and, intriguingly, Brookfield had a newspaper named the Brookfield Argus at one time in its history.
I would recommend you consult any genealogical or historical societies that operate in Linn County. I would also recommend you consult the "Compendium of History and Biography of Linn County Missouri," written by Henry Taylor and published in 1912. Depending upon how much time you have on your hands, you might also start trolling through newspaper microfilm dating to the time your ancestor would have been of military age, to see if mention of the Argus Rifles comes up.