Which of these is NOT a proper time to apply the parking brakes?

Applying parking brakes when the brakes are very hot is not advisable due to the risk of damage to the braking system and reduced performance. When brakes are hot, they are more susceptible to wear and warping, and engaging the parking brake can lead to sticking or overheating. In contrast, applying parking brakes on a flat surface is acceptable because it firmly secures the vehicle. It is also appropriate to engage the parking brakes when parked for extended periods, as this helps prevent the vehicle from rolling. Finally, applying parking brakes while the vehicle is in neutral is also proper, as it allows for securing the vehicle without any strain on the braking components.