Well, here is how I would go about it. Check with the local historical society or library to get a list of Searcy County companies and the regiments they served in. And these lists can also turn up in odd places (Independence County's list of companies came from a courthouse monument). You can then go to the "Gerdes" site and check the rosters for those companies and look for a John Johnson of the right age at the time of enlistment. Then compare the rest of the company roster against the census records from 1860. If you have your man, there will most likely be a substantial number of soldiers within the company from the same township. Good luck, I know what it is like to look for Johnsons.

David