i hate to burst your bubble. but the cap is doing more harm. A cap is being used as a bandaid. its covering up your electrical voltage problem. While your eyes are seeing dimming with the cap out, you can clearly see you are having a problem, but with the cap its covering up fooling you to believe you have solved the problem. In the long run, your batteries will die out sooner, and your alternaot is taking a beating from trying to keep up the charge for the demand of power. my suggestion to you is to start by getting a deepcycle battery, then upgrade your wires(with a thicker guage) coming from your alty to bat(as well as grounds). then if problem still occurs, upgrade to a higher amp alternator.
so long story short solve the problem, dont cover it
edit: i realize i didn't answer your intial question sorry about that. but my response should still help your other problems