In 2 point perspective, do both vanishing points need to be on the horizon?

Unless you want to treat a vertical as your horizon (which is acceptable but makes for a weirder image, occasionally used in science/space fiction illustration). You can be more dynamic by rotating it to a non-right angle, but basically the vanishing points should appear on the same hypothetical straight line (go wild and use a curved line just for fun resulting in no straight lines).

Only if you want the picture to look like it's being viewed from eye level on the ground.

If the vanishing point isn't on the *horizon*, then the surface you're looking over won't look *horizontal*.

Try it and see what effect you get.