How do you intuitively see how the $\hat{Z}_1$ and $\hat{Z}_2$ construction is a voltage divider?

You can apply the voltage divider equation anywhere you are looking at a voltage in between two circuit elements, if you know the overall voltage drop across the whole network. It doesn't matter if there are additional wires or terminals sticking out at the places you're looking at the voltage (if they are just open circuit). Sometimes it takes a bit of practice to acquire the intuition about where one can apply the voltage divider equation, but it will soon seem more obvious.