* Electrical System Shock: A massive impact could cause a surge in the electrical system. This surge might be enough to trigger fault codes in the engine control unit (ECU) or the anti-lock braking system (ABS) module. These codes, stored in memory, would then illuminate the respective warning lights. The problem isn't necessarily *in* the engine or brakes, but a false reading triggered by the electrical jolt.
* Wiring Damage: The pothole could jar or even sever a wire related to the engine or brake systems. A damaged wire, even if not directly impacting the mechanical operation, could send a signal to the ECU or ABS that is interpreted as a fault, causing the lights to turn on. This is more likely than a pure electrical surge.
* Sensor Malfunction: Sensors throughout the car monitor various parameters. A jolt from a huge pothole might damage a sensor, leading to a false reading that sets off a warning light. For example, a damaged wheel speed sensor could trigger the brake light (ABS-related).
However, it's important to stress the improbability. These scenarios require an exceptionally large and violent pothole, and even then, it's more likely to cause other, more immediately obvious damage. If the check engine and brake lights come on after hitting a pothole, it's *far more likely* that there's actual damage to the engine or braking system, or related wiring, even if not immediately apparent. The lights are a warning sign that requires investigation.