[dmjlambert]

As VetteVet mentions "The white wire is the grounding side of the circuit and it runs from the headlight switch down to the harness to the drivers side door switch and under the sill plate back up to the dome light. "

If you connect the white wire to ground the dome light will light up. So, I think the things you mention are correct, such as "I didn't think the white wire would do anything until switch is turned to the ground position."

There are a couple methods grounding the white wire happen. One is if your headlight switch is rotated all the way counterclockwise you will feel a detent and the dome light comes on. This is assuming the headlight switch is installed and has a good switch body to cab ground connection. Another way is if your truck is equipped with switches in the door jambs, those have a single wire going to them and the jamb switch shorts the wire to ground. I found it necessary to remove my jamb switches and clean the contact surfaces with a wire brush to get them working.

You will notice a voltage on the white wire if it is not grounded. So you're headlight switch is either not grounded, or the dome light switch in it is not working, or I think the most likely thing you have going on is a connection at a switch or at a connector is not good and clean and connected. Check all the connectors and clean them up and plug them in again. It is possible when a connector is pushed onto a switch or into another connector, the terminal inside the connector may pop out of the back of the connector. So inspect for that sort of thing happening and re-seat terminal if necessary.