I had that same problem since I got mine 2 years ago. Then somebody I know with a '97 GT who also had the same problem played with his switch a little bit and found the problem. I did the same to mine and found the same problem too. Both of us also didn't have working rear running lights. Check your tail lights to see if they don't light up.
I still have this issue. When I turn on my lights, I pull the switch all the way out and push it back in just a little bit. I mean very little bit. My dash then lights up and headlights go out. I have to keep pushing it in & out, a little bit, until both are working at the same time.
It's a hassle. If you don't find any other possibilities, you might want to try jerking the switch around like we had to.