2007 pt Crusier charging problem

I tested the black one and it was dim and when I put the light on the green one it was bright and the green wire didn’t have a fusible link and the black wire had two. I tested it not running should I try it running?

I had to repair the black wire because it looked like it was pulled on and the wire Insulation was ripped off the wire or maybe it got hot and the wire melted from the Insulation but I cut the damaged wire and ran new wire. And I suspected the alternator I bought was bad because it’s happened to me before so I took it back and got a brand new one but I guess it must be something else if it’s having the same problem.