I have 1996 Lumina.
I have exactly same problem as you have.
My tailights, parking lights in the front and dashboard lights including around heateing control and radio are not turning on when the headlight switch is turned on (both park and light).
The bulbs are ok. The break lights do work.
I have also found several similar problem on the internet.
One of the site suggested replacing Headlight switch.
I have ordered a switch from Autozon (70.99 plus tax and shipping at around $82), but it did not fix the problem!
It appears all the fuses are OK, but it has so many fuses and do not know exactly which one in particular should be checked.
If you get any info, please share with me.
Lee