HI!
A capacitor will not help your problem in this case. I say this because your problem is due to CONSISTENT low voltage. If your headlights are on, you are continuously drawing the voltage down. A capacitor will only store current to supply the voltage for a short period of time. Also, power flows in more than one direction. The capacitor would be supplying current to your headlights, until it reaches the voltage that the system would initially be at without the capacitor.

To fix even that problem, you'd have to install a diode to the supply wire for the capacitor, this way the current wouldn't flow backwards into any other devices.

And, with that done, your capacitor would have to be of significant size, say 1 Farad, to supply your Empeg with enough voltage for more than a few seconds.

A fairly costly issue. Maybe your Ground, and your 12V supply should be connected directly to the battery with, say, 12 gauge wire to minimize voltage drop. This could make a big differencre. But watch out for ground loops, you'd have to run the ground for your deck and amps to the same point to eliminate alternator whine.

Hope this helps clarify capacitors a little!??