Sounds like your ignition switch is done. You measured 12 volts at the white lead and when you turn it on it dropped to 6V... that means the problem is in the swith. By spraying cleaner inside the switch i think you might have burned it out. The only way to know for sure is disconnet the igntion switch inside the headlight, then on the harness side your gonna need to jump the white lead to the brown... that will bypass the ignition. Then measure the volts at the coil, it should match your battery voltage...maybe not exact but only a few points off.
