69 barracuda convertible has no dash lights or inside lights when you open the door
The fact that pulling on the harness works makes one suspect a loose connection... unfortunately, on the dash, it probably means a loose pin on the circuit board. I suppose it could be one of the wires in the big multi connector isn't fully seated — the female sockets aren't attached to the plastic plug, so they can come loose independently. Look in the FSM for the pin-out and see which one is for interior lights/instrument lights. Maybe you can reach up and shove it in from the back.
If it wasn't for that, I would suggest the ground on the door switch... corrosion, or new thick paint.