First trick is to re-ground the battery with the same gauge wire you ran to the amp. Usually dimming lights is a difference of potential problem, say you run 4awg back and are still using the factory 8awg return to the battery. Easily overlooked in the circuit. Also, if you do the math 1000wRMS/14.4 volts = 69.4amps. Depending on the car, most cars use a 70% load with lights on/heater on. Say if you had a stock 100amp alt. you only have 40amps left to play with. Not enough for sure, and theoretically it only gets worse when your voltage drops below 14.4 (volts to amps trade off). Unfortunately the 1000/1 is a monster and energy hog and to do it correctly the whole charging system needs an upgrade, starting with the alt, the the battery, and maybe a capacitor to stabilize the voltage. Good luck!