Battery light issue

I have a 2008 with a 4.0 and the battery light is on, the alternator is charging but as I was investigating there is a broken wire in the harness for the green plug, there are 3 used spots on the connector but 4 wires in the loom I have no idea where this broken wire should connect any help would be appreciated

 

The 4.0L only has 3 wires in the alternator connector.

Pin 1: White (Voltage Sense) (S)
Pin 2: Light Green (Ignition Power) (IG)
Pin 3: Not Used (M)
Pin 4: Grey (Warning Light) (L)

View is looking into the connector, terminal designations are also on the alternator.

 

Thank you for the response. The three wires are there and have continuity from the alternator plug to the plug in the fuse box, there is a fourth wire in the loom that is broken and that is the wire I do not know where it’s supposed to connect.

 

The white wire is the one I’m talking about.

 

Looks like you have the factory white wire still in the plug.

I don't know what that exposed white wire you have is for.