You can do the half phase rectifying if you want but that's not really going to give you full that regulation on half of the system you're only going to catch the up or down wave of the spike.
Just find a capacitor that's about the size of a D battery are bigger IV been used starter capacitors for electric motors as long as it's the size of one or two D batteries it should hold enough current and voltage to suppress voltage spikes and give consistency in the headlights at idle.
If you're not using a battery you can put the capacitor after the regulator but it must be before it if you're running a battery otherwise the small resistor on it will drain the battery.
If you want to do more research I suggest you go to the website.
All about circuits. Com
It will instruct you on how everything works from basic to the latest technology out there(edited)