That would be a well, not a privy. Rural areas very rarely ever brick-lined a privy, that was typical only in a city lot where there wasnt room to move the outhouse around as it became full. A privy wouldnt be around a well either.
If you want to find the old outhouse (there were likely multiple locations), you have to do some deducing and probing. Think about predominant summer wind directions. The privy would likely be somewhere downwind of the house. It also wouldnt be too far from the back door because how far would YOU want to go through cold, snow, wind, rain, at night? Lastly, look for depressions in the ground where the backfill would have sunk slightly over time (not always though). Once you think you know where it might have been you have to start probing. Keeping in mind that the hole was likely only about 2 - 3 feet in diameter, so if you arent probing in a tight enough pattern, you can walk right over the top of it. When you probe you are looking for 1 or 2 things. First, you cant hide a hole. The fill will always be looser than native soil so the privy will feel VERY easy to probe. Next (not always) you are feeling for your probe to make contact with solid items. With practice you can learn exactly what glass feels like as well as unbroken bottles.
