68 Barracuda Instrument lights not working

If the car wasn't being daily driven, the headlight switch can become corroded. You can try operating it again and again to try to clean the contacts (push/pull, twist/twist, over and over), or just buy a new switch.

The fact that the gauges work is great, and suggests the cluster plug is OK. Although every function is a separate pin, and any one pin could break loose at the solder connection to the circuit board. Let's hope it's not that.

If you have an inspection mirror on a stick, get a powerful light and see if you can inspect the wires leading into the plug. The individual wires end in copper connectors that just slide into the plastic plug — when reseating the plug, it is possible that one or more connectors doesn't seat — it just gets pushed out the back of the plug by the pin. This is obvious if you look at it.

You don't want to be pulling that whole plug if you don't have to — every time increases the chance of breaking a pin loose.

I would start with the headlight switch. You might also look at the hi-beam floor switch, and try the hazard switch to see if it works. It almost always has the corrosion issue since it is hardly ever used.