Hopefully it is good now. That ground for some reason was the ground needed for the light to function. Your jumper from door striker to dead side of bulb made a substitute ground and the light came on.
The way I am understanding that small wire is in the same way most warning light systems work. You have power supplied from key switch, through bulb, to alternator field. Turning key on lights bulb because circuit is completed through alternator field to ground (the ground you were missing). Once engine starts and the alternator starts spinning it will generate voltage and you will get alternator voltage (13.9v) on the terminal (rather than it being a path to ground) and feeding back into the bulb which was fed battery voltage but now has 13.9v. So you actually have no voltage drop across the bulb to light it because battery voltage is 13.9v on one side of bulb and 13.9v on other side of bulb fed by alternator small wire terminal. If alternator goes dead then that 13.9v goes away on alternator terminal and current will once again flow from battery, through ignition switch, through bulb, to terminal on alternator and to ground and light comes on. If bulb is open circuited you don't have path from battery to alternator field and this is why an alternator often does not charge until bulb issue is fixed.