It will be the only wire with 12v at the main 6 pin plug, when you test it with a test light. Generally there will be a white wire to every coil, daisy chained along, which will be 12v.
Running it straight to the batter will be fine, all that will do is aid in fixing perished wiring. If there isnt heaps of resistance across that circuit or its not showing low voltage I wouldn't bother.