Problem solved. I checked continuity from the dimmer to the plug and that was fine. Checking it from the dimmer to the metal frame of the light panel was not, though.
I noticed that my light panel had surface rust all over the upper surface of it. Not deep, but since this surface isn't painted by the factory and the car sat for several years, a thin layer of corrosion built up. I could get the lights to go on if I grounded the individual bulb after removing from the socket, but not when I installed them and grounded to the frame. Even sanding a clean surface on the frame and grounding it wouldn't work. I ended up having to sand very, thoroughly, the inside socket portion of the frame where each bulb fit in. After that everything worked.
Thanks, everyone, for your help in this. CC.com comes through again.