I'm afraid I don't quite understand what you are asking.
When setting up the Chevy starter with a dual solenoid system the 'S' terminal is jumpered to the 'battery' terminal with a short piece of wire. Does that sound like the wire you are asking about? If it does, you do not need it.
The starter in your picture appears to have all the necessary connections (the ignition switch wire connected to the small 'S' terminal and the positive battery wire connected to the large 'battery' terminal). The only thing missing is a proper ground. The starter was designed to be able to ground through the engine block. However, connecting a dedicated ground wire directly from the negative battery terminal to the case of the starter can eliminate grounding problems. The long bolt sticking out of the main starter motor housing (in your picture) would be an excellent place to connect a dedicated ground. Ideally you would want to use the same gauge cable for the ground as the battery cable, but most don't have one at all.
Here is a picture of Fatman's excellent starter set up with a dedicated ground. (His is also set up for dual solenoids. Your red wire should run to the ignition switch not jumper the two terminals.)