Somewhere in the power chain are wires that are too small. The "disco-ing" of the lights indicates a weak spot somewhere, whether it be undersized power or ground to one (or both) of the amps, faulty main ground, or any other number of bad chassis grounds. Check/replace all of your wiring before you drop the money on a cap-- the wire will be money much better spent. Honda uses 6ga from the alt to fusblock and fuseblock to batt + (to carry the 65-70 amps from the alt.) while your system @ peak draw is looking for something in the neighborhood of 100-120 amps. The Honda main ground and block grounds are also a wee bit undersized.

I'm all 2ga, including grounds, and while I can get massive voltage (drops to 12.5v or so, w. 135amp alt) dips at high volume, the lights won't dim at all. Big wire is your friend.