Wow!
A lot of responses for you on this one.
Let me ask:
Is the headlight switch new?
67dart is correct, the headlights don't go through the fuse box, but the switch could be faulty.
We've established that it is properly grounded.
Two things to look at . First is the fuse-able link on the firewall , I believe if it blows that it will take out the headlights.
Second thing in the "ampmeter". These are notorious for burning out or even burning up. You can bypass it by it by connecting the two wires together...DISCONNECT THE BATTERY FIRST.
Your fuel gauge:
The new tank sending units that you can get have their issues, but the problem is likely in the dash. There's a voltage limiter in the cluster that drops the current to 5.5 volts for the fuel gauge. With a little thought and examination, you can "bench test" it. Look at the printed circuit board to follow the current path to the gauge, grounding .........maybe we get you through the headlights first.
I have a complete 64 Barracuda gauge cluster, if needed