[RedDevil]

Why would a racing car run the alt from the gearbox instead of the engine, and where in the gearbox could it hook up?

Well, not having the alt in before the clutch means that the rotating mass on the engine gets less. It could rev up or down quicker between gears.
The input shaft will have to change speed too though. The alterrnator could double as a motor to speed up, or draw extra to slow down the input gear shaft when shifting gear.

If the alternator is on the output shaft then its speed would equal that of the car, and possibly it would only provide full power at top speed while at lower speed the lesser drag means quicker acceleration.

Neither setup seems particularly fit to reduce fuel consumption in a road going car.

The Insight has an electric motor/generator that doubles as a fly wheel. But the Prius has electric motors and generators incorporated in its 'e-CVT' planetary gearbox system. The racing Prius.