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