Trigger Context Property driver to update on active camera change

I think that changing the active camera should trigger the context properties to be recalculated.

I have a scene with a vehicle and a bunch of cameras for different angles. I have a driver on the front tires to turn them based on which camera is active.

This works in the render, but changing the camera doesn't cause them to immediately update. I can press left/right arrow key to get it to update, but would be cool if it was automatic.