Alternator wiring diagram?

In replacing the alternator, we have to splice the wires for the electrical hook-up on the side. There is 1 small white wire and 2 thicker black wires. The black wires look to be the same size and we were unsure of how they connect.

The alternator in the truck was giving me problems (gauge needle was bouncing back and forth, headlights were dimming/flashing, checking with voltmeter showed an inconsistent flow of power would spike to 14 then down to 11 then back to 14. I took the alternator to Auto Zone and they tested it and said it was bad. I purchased and installed a new alternator but when I checked it with a voltmeter it did not appear to be charging. I took the alternator back and had it tested and it passed. I was told to replace one of the plugs (3 wire plug that goes to the stator) I replaced the plug but still no output. I have since noticed that there is a wire broken off near the fender well, I traced that wire back to it's source and it goes to the 3 wire plug I replaced. I don't believe this wire is the reason for the lack of output on the alternator because it looks like it's been broken off for some time. Any ideas on what this problem could be? Thank you in advance for any help you may be able to provide.

According to the picture the wire jumps over to the regulator but on the truck it runs back up the wiring harness at least a couple feet before it's broken off. I don't understand why it would run back up that far just to come back to the alternator. Do you think this wire would keep the alternator from outputting power? I also checked that wire with the engine running and it was carrying about 1.05 volts. Thanks for the quick response.