I assumed he meant it wasn't coming on...since there is no info on what this vehicle is, we'll deal in generalities...
the batt. or charge light has 12v pos fed to it, and that 12 v goes through the filimant sending a pos signal to the alt which starts its charging circuit. the wire between the alt and the light is a pos signal when the charging voltage is above battery voltage, and its a ground signal when the charging voltage is below battery voltage (which is what turns the light on when there is a problem). If you removed the light, put it back, it needs to be there for the system to operate correctly. No, you cannot just run a wire without the light in place, because it needs positive at startup, sends pos back when functioning, and sends a ground back when not functioning (like engine off) so without the bulb, it would just be a short circuit.