First thing I would try with your headlight and dash light problem is to pull the switch and swap it with the one from the other '66 you have.
As I recall the light switch is unique to the '65 and '66 years and while they look identical to other years, internally they are different. Possibly someone has swapped in an incorrect switch?
Second thing is to ensure you have a GOOD ground wire from the back of the instrument cluster to the body of the car. I can tell you from bitter experience that while what connections you have might look good, they can give endless problems.
Do you guys know which lights should be on in the low beam position? Top or bottom? Bottom lights are low beam. Top lights are high beam but BOTH top and bottom should be on when high beam is operating
Let us know how you go
Ian

