Dome light issue

I think you may have very high resistance in your circuit. A meter can detect voltage even if there is no amperage. I'm assuming you are connecting the meter across bulb terminals, try hooking one lead to chassis ground somewhere and the other on your bulb B+ terminal and see if the voltage goes closer to 12 instead of 11.
Ok ill give that a try. Should be able to ground on the mount for the housing. Which is the B+ terminal? Mine was labeled 2 and 3.