Yeah, I didn't expect you to come back to the cap thing.
But since you did...
If your headlights are dimming it means the entire vehicle system's power is fluctuating. To treat only the one symptom for the headlights is rather ludicrous. The voltage regulator at the alternator is working overtime to try to manage the spikes in system power and that will lead to premature failure of the regulator at some point. A cap will help the regulator out by smoothing out the power demands a bit so the regulator doesn't have to work as hard. Other more discreet circuits (like the vehicle ECM, TCM, head unit, and anything else with a board) are also going to be sensitive to the change, and although they all have some capacitors onboard to to protect them, you have to realize that ALL of the capacitors of EVERY piece of equipment are all wired in parallel on the same circuit, just at different points. Those ECM, TCM, etc. caps are now supporting your audio amp just like an external cap would. So they have diminished ability to help with their own meager power draws because they are getting sapped by the audio amp.
Using a cap isn't about theory crafting, there is actual electrical math behind it. The reason that a good JL amp will need less external capacitor that a Boss amp is because the JL has more internal caps on the board. When you do the math to determine the need for capacitance, it works out to roughly 500w needs 1 Farad. So the JL 600W amps in our example need 1.2F-1.4F (when you consider amp efficiency, more of that later). You can tell just based on physical size, that when looking at the board of that JL amp, it does not have 1.2F of capacitors onboard. I actually tried to find the board specs of the caps on those amps, but no luck. I did find some images of other JL amps though. And they do not have 1.2F worth of capacitor bank onboard.
Finally, mathematically consider that this is all about energy in the system at any given time. Literally, the amount of electrons flowing around. If most A/B amps are 70-80% efficient. Most D amps are closer to 90%. This means that when the bass hits at say 40Hz and your amp is trying to supply 600W to the speaker, it actually has to pull 600W / .85 = ~706W from the electrical system. To do this at 14V will require 706/14 = 50.4A. If the system voltage has dropped to 12V, it requires 706/12 = 58.8A. Now, again without a cap, that means that a pair of these JL amps will be trying to pull almost 120A. The vehicle has 110A alternator output. So the other capacitors on other equipment are definitely getting tapped to supply this juice. Also, the car itself requires roughly 20-30A of power for its electrical system. So you are really only going to get a burst of about 80-90A. So that goes back to the amp, and mathematically reduces the actual power output at the speakers: 90A *.85 (amp efficiency) = 76.5A @ 12V = 918W. 918W is all that poor amp has the electrons to provide to the speaker. So without an additional cap, you just dropped the power of your system from 1200W to 918W. Maths. Also, that load has drained every capacitor onboard on every piece of equipment.
One last little bit is that the voltage regulator and alternator are not able to provide power on demand as quickly as a capacitor. Electrons move way faster that the voltage regulator's circuit computes demand and output. Capacitors have the electrons necessary to meet that demands.
To summarize, dimming headlights are a symptom of a greater system problem and should NOT be addressed independently. The entire electrical system of the vehicle needs to be addressed because there is a larger problem that will eventually manifest itself somewhere in the system. It's not just about the amp's output or heat. It's about a well designed and functioning electrical system as a whole.
Also, for reference, an older JL 1000/1:
(NOT 2.4F worth of caps)
And an older 500/1:
(NOT 1.2F worth of caps)
