I'm thinking that they should travel around the perimeter of the village, and occasionally come back to the center, instead of wandering around aimlessly. Of course, finding a baddie will always have higher priority than the patrol.
Upon spawn, look for the bell.
Randomly elect to find the furthest house in any of 8 directions. (North, south, east, west, NW, NE, SW, SE)
Check the furthest building in each direction, randomly selecting clockwise or counterclockwise.
After one loop, it returns to the bell for a moment. Repeat.
This way, the golem will tend to keep searching the more dangerous areas, while still coming into town to see if there's any trouble that got in already.
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