Either can happen. I do notice if you have a lot of paths it tends to make them plot where the previous villager was more often but maybe that's just my town.
Random. They can plot anywhere, though in my experience, they tend to favor the previous villager spot. If you want them to plot elsewhere, the safest thing to do is to plot reset.
From what I read on this site and others before, Amiibo invited villagers tend to move where the original villager was kicked out more often than a different spot. However, they are still able to plot at other places, but at a significantly lesser chance.
In my experience, they plot either in a random spot, or one square along from the previous animal. Never in the exact same spot, it's always been one square to the left, or one square down etc.
I don't have paths by the way, so my animals aren't restricted where they plot.