I did not see this question here after a search but I was curious to know how do you change the direction of Illustrator's perspective grid from the
To something like this:
It's possible to alter the grid into any number of settings. Although it may require you to rethink where your horizon is. For example, in your sample the horizon is on the right. It will need to be either top or bottom for the Perspective grid to work better.
There's no easy way to explain how to configure the grid, other than to simply show the settings under View > Perspective Grid > Define Grid.
Which creates a grid similar to.....
It ultimately comes down to using the Perspective Grid Tool and moving the grid points around until you get what you are after. Then some conceptualization to understand that the grid is, in many cases, not going to be 100% visually what you expect. For example, your sample has a hole at the vanishing point. You can spend time trying to define that hole exactly, or you can simply choose to draw objects on the grid and leave the hold yourself.
I'm not a huge Perspective Grid user and tend to stick with it for simply 1-point or 2-point perspective. As soon as I need to start getting into 3-point, I look for a better dimensioning tool (3D) with vector output if possible.