Charging problem

Well, when I drive it the charging system seems to work fine, the headlights on and the heater blower turned all the way up. Then when I come to a stop. I hear the blower motor slows down the lights dim slightly and the voltmeter drops just a tad bit then it recovers. But every now and then I will be driving it and the voltmeter drops maybe half way and then usually it bottoms out and runs directly off the battery. I tested the alternator. Test okay. They said the problem was in the computer. Okay, so they know everything right? Wrong! A new computer cost $300.00! Could not find a used one. Lucky for me this is what I figured out. I thought maybe there was a loose wire somewhere. After almost pulling my hair out. On top of the alternator on this there is a small black box with two green wires and a thick red one going in and the red one going out. What is in that little black box? Something must move or switch? I did not want to break it open before I find out exactly what goes on in there. Thanks