Ok if the tail light circuit works, that circuit is actually where the headlight switch "gets" power for the dash lights. Power goes through the switch to the dimmer control, OUT the dimmer control on TAN, and down to the small "inst" fuse which is all the way to one end of the fuse panel.
So with the lights in park or head, turn the dimmer all the way to left before the dome switch clicks.
Then probe the INST fuse and see if you have power on both sides of it. If you don't, trouble is up there in the headlight switch. "Wiggle" the dimmer control back and forth as they get dirty and develop "bad" spots. If that does not work, you likely have a bad dimmer control on the switch. HL switches are not expensive, and are available at "real" parts stores.
The dimmer is a different matter. Sometimes the door switches get crudded up. The headlight switch MUST be grounded to operate the dome switch on there. Access one of the switches, like the drivers door, and see if you have 12V from the switch to ground. Try grounding that wire.
If no power, pull the dome bulb and probe both contacts for power.
If you don't have a factory shop manual, download one, free, over at MyMopar:
http://www.mymopar.com/index.php?pid=31
Also from MyMopar is ONLY the wiring diagrams but which are out of the shop manual........this saves you from pawing through a bunch of pages
mymopar.com/downloads/1967/67_Dart_Charger_Wiring_Full.pdf
And there are AFTERmarket wiring diagrams. These are sometimes easier to follow than factory but they are often incomplete and often leave out some terminals and connectors
http://www.mymopar.com/downloads/1967/67DartA.jpg
http://www.mymopar.com/downloads/1967/67DartB.jpg