In Sweden, where people drive on the right, I have have heard that you should walk on the left side of the road if there is no sidewalk. But, when on a sidewalk or footpath people will keep to the right.
Also confusingly, when Swedes are about to make a left turn they keep to the far right instead of the more logical left, and vice versa.
With the four-way you describe, I would usually expect to see a single light, with it blinking yellow on the primary route, and blinky red on the secondary road.