New dash bulbs not working

Ok, quick update. Cleaning the black bulb holders did NOT work. I also pulled all the bulbs out of a '73 dash I have and swapped them in, nothing changed...so I'm assuming the new bulbs are good. One new thing I noticed though -If you have a turn signal on, then turn on the headlights, the turn signal on the dash reverses direction. So if I have the right turn signal on, then turn on the headlights, the right indicator on the dash will stop and the left one will turn on, but the exterior turn signals will still flash on the right side. Could the problem be the headlight switch? I don't understand how that could effect turn signal operation though.

*Car is a 1975 Dart custom if that matters*