The big single wire goes to the battery +. The plug with 3 smaller wires is usually the place that gets messed up. The wires flex a lot right where they enter that plug. Over time the strands break off inside the insulation and then you've got a problem. Regardless of what wire(s) are messed up, just pick up a new alternator harness and be done with it. The part you need is called "WIRE, ENGINE, N" Toyota Part number 82124-28034 available through Tonkin Toyota
for about $35. If your new alternator is bad, you wouldn't be the 1st van owner that has happened to (it's not all that uncommon for those cheap "lifetime" alternators). Also, keep in mind the guys at the parts store don't always know how to test all alternators correctly. It's possible the problem was always in your wiring and the so called "problem" with your alternator was just the idiot conducting the test
PS: Here's a picture of that harness "WIRE, ENGINE, N"