Here's the quick answer:
The small wire goes to a switched source of 12 volt power. One way is to connect it to the black wire that used to go to the old VRR. Another way is to look on the left side of the frame there for another connector that also is switched and fused.
However........
The far superior way to connect that wire is to set up a relay taking power directly from the positive terminal of the battery and hooking it up to that. Make the relay triggered by the same wire that you would have otherwise run to the alternator.
The benefits are thus:
The current supplied by any of the stock wires on the ST, goes through a long path up to the switch and back to the fuse block. It includes a bunch of connectors. In time the connections corrode, lowering the volatage available to the alternator. Also, there are voltage drops also because of the long path the current takes and the relatively small size of wire. It works, but only just. And as time goes on, you'll eventually see your alternator output voltagef drop.
I hooked my 40 amper up to the original wire feeding the VRR. I got 14.2 volts with the new alternator. Then, though the years, I saw my voltage drop slowly but steadily. Finally, frustrated with the situation, I analyzed the situation and realized that the magnetic field in the alternator was created by the current going to the small wire at the alternator. Less voltage means a weaker magnetic field which means lower ouput. So I did the rewiring, a simple task, and found I now got 14.4 volts. Up from the 13.6 it had dropped to and up from the original 14.2 as well. Nice.