Typically, the warning light has a ~100 ohm resistor across it to guarantee that the alternator receives it's 12 volts so it can start. One side of the light connects to a switched ignition feed. The other side, of course, is the alternator "I" terminal. Normally this is at 12 volts keeping the light out because you have the same voltage on either side of it. When a fault occurs, the "I" terminal goes to ground illuminating the light. There is no guarantee this wire will tell that the engine is alive or dead, it will tell that the ignition key is in the "on" position or not.