With passenger door closed and both courtesy and dome lamps "off", I would expect to measure 12V at the white wire connector that mates with the switch on driver side.
The body of the switches will be ground. Screwing them into the door pillar should tie the switch bodies to ground. This seems to be working on the passenger side.
If the lights are "on", I would NOT expect you to measure any voltage as the current flowing through the lamps (resistors) will drop all the voltage.
If you think the driver-side switch may be "bad" (ie is always "open"), you can simply ground the white connector to bare metal on the chassis and the lamps should illuminate. If this doesn't turn the lamps on, then yes, you may have an open wire or bad connection on the other end.
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