Pull the connector plug off the dimmer and get out the voltmeter. See if you have 12 (or so) volts from any of the terminals to ground. (If not, skip down.) If you do, try running a jumper wire from that terminal to the other two (one at a time). If you get lights, then the problem is either the dimmer switch or the connections.
Clean the connections up with a little scotchbrite pad (or similar) and clean the connections on the switch too. Use a tweezers to get up into the terminal with the pad. (Fine sandpaper may do, but avoid steel wool. You don't want a lot of shavings in the connection.)Bend the terminal tabs up a little to make sure they get good contact then plug them back onto the dimmer. Still no lights but you got lights with the jumper? Then it's the dimmer switch.
If you didn't get 12 volts at one of the three terminals on the dimmer make sure the light switch is on and test it again. Still no voltage? It's either the headlight switch or the wire from there to the dimmer (assuming the headlamp switch feed wire is OK because you are getting dash and other lights).
It's a little tougher to test the headlight switch because the wiring is all stuck up under the dash and hard to unplug. It might be easiest to remove the switch from the dash. (Should be a little trigger or pushbutton smoewhere on the body of the switch that allows you to pull the knob and shaft out. Feel around the body of the switch under the dash and see if you can find it. If you can get the knob and shaft out you will still have to unscrew the collar that holds the switch to the dash.
Once you get the switch out, you can easily see how to unplug the wires from it. One wire should be hot. (Measure 12V or so to ground.) The others go to the headlights (actually the dimmer) and to the parking lights, dash lights, etc.
Since you say you have dash lights, etc, you must have a good feed wire, so use the voltmeter to find it. Then try jumpering from it to the various other teminals and take note of which circuits light up. If you can get the headlights to work this way, the headlamp switch is probably bad. Before throwing it away though, try cleaning up the terminals the way you did the dimmer switch terminals.
Hope this helps. The instructions are a little generic because I am not sure what the circuit or the parts look like for a '67, but I've had a '70 apart recently and that should be close.
I would bet it's the terminals on the dimmer switch. They catch a lot of crud down there on the floor. (Especially on a farm truck, but let's not contemplate that...)