If you are still wondering about the front driving lights, they are working properly. Though they are commonly called running lights, they are actually just parking lights. They only function when the light switch is pulled to the first stop. That gives you rear parking/tail lights and front parking lights. When you pull the switch all the way out, the headlights come on and the parking lights in the front go off. I had the exact same question on my 58 Burb. I even went and bought a new light switch from Jim Carter just to have the same issue persist. I posted the question on here and was straightened out by a fellow bolter. If you do a search on here for parking lights/driving lights you should find some info. There is a way to create two small bridge wires between the posts on the light switch to keep the parking lights on when the headlights are on. Its a simple fix.
I'm not sure about the dome light. I think it should work when the lights are off. Best to post the question in the Electrical forum.
I enjoy following along on your build. You are doing great work!!