It can be done easily with Keyboard Maestro ($36).
Create two macros, with whatever keyboard shortcuts you like, one for focussing the lefthand pane, and another to focus the right one.
Use the Move and Click action to Click the Left Button relative to the Absolute Postion.
You need to set the x, y coordinates according to the size of your display. The height isn't too important (I just used the halfway point), but you'll want KM to click near to the sides of the display, so the clicks will always be in the correct pane, even if you resize them.
Obviously, $36 is a lot to fix one thing, but KM can do a lot of useful stuff, so you will probably find it's worth it, especially if you like doing everything with shortcuts.