In a 1969, the left door jam switch controls and applies the ground for two circuits, the interior/courtesy lights, and the key buzzer switch. In the interior light circuit, the headlight switch can also ground the ciruit by turning the knob all the way past the detent. The interior light grounds are white. Interior/courtesy lights are fed 12 V pos. at all times via orange wires. In the key buzzer circuit, the left door jam switch will ground (through the black wire) the key buzzer switch (in the steering column by the ignition lock), which if there is a key in the ignition lock depresssing the contacts will activate the buzzer. The right door jam switch only has the white interior light ground wire since the driver rarely exits though the right door forgetting his keys.
. So if your dome light is staying on, the white wire is grounded somewhere. It could be in the door jamb switches, the headlight switch, or any of the white wires could be shorted to ground. A remote possibility could also be that the black wire for the key buzzer switch is grounded, but in that case the buzzer would sound any time a key is in the ignition with the door open or closed.