thrs no use in adding a capacitor if ur battery/alternator combo is weak.
ur lights and amps are cuttng off because u cant power em properly, either ur battery is weak; try recharging, or it just cant provide enough continous amperes when the car is OFF.
if the car is on, and battery is charged normally, and u still cant get enough amperes, get a bigger battery, followed by a capacitor, followed by a bigger alternator.
thou if ur system was working fine before, it should be fine with a fresh or full charged battery.