Q: “When you are running a road course, how do you determine when to downshift?”
A: The simple and clear answer on when to downshift for a corner is this: wait as long as you can during the braking zone approaching a corner to downshift, but it must be completed (with the clutch fully engaged and your foot off the pedal) before you begin to turn the steering wheel.
The reason for leaving it as late as possible during the brake zone approaching a corner is to minimize the engine braking effect, and the possibility of over-revving the engine from an early downshift, as well as minimizing the chance of un-balancing the car from the sudden extra deceleration from the engine braking. The reason for ensuring your downshift is completed before turning into the corner is because letting the clutch out and engaging a lower gear while turning can cause the car to spin (or nearly spin). If you’ve ever let the clutch out while turning and had the car lurch and have the rear-end (in a rear-wheel-drive car) begin to skid, then you know what I’m talking about.
Think of the approach to any corner than requires slowing down as a brake zone. You want to do all of your downshifting during the brake zone. And if you’re asking, “I have to brake and downshift at the same time? Isn’t that a lot to do all at one time?”, then you need to learn or refine your heel and toe downshifting technique.