Advanced lighting issue
 

I have a 91 d350 dually. Recently the parking lights quit working. They blink on when the switch is in the middle position between off and parking lights, and again between parking lights and headlights. But do not work in either on position. I bought a new switch, it does the same thing. So I tried another new one, same thing. I'm pretty baffled. I know they are getting power, and grounds work because they all come on, just at the wrong time. I appreciate any help. Thank you!