You may have it wired incorrectly or you may need a dimmer switch. Here is a close up of how the headlight switch & dimmer switch should be wired:
The tail lights are powered by the orange wire to the switch and it has a fuse on the fuse panel. If that fuse is bad, the dash lights won't work either. There are 2 hots running to the switch - the orange and the red wire. The orange wire gets power through a fuse that also powers the brake light switch, the dome light and the glove box light. Notice the junction of the orange wires in this diagram right above the headlight switch. http://www.tocmp.com/tOCMP/wiring/5765wiring%20diagrams/Chevrolet/MWireChev57_3WD-057.jpg
The red wire powers the headlights and the orange wire powers the tail and dash lights through the switch. When the switch is pulled out, the green wire goes to a 3 amp fuse on the fuse panel to power the dash lights.
The red "hot" comes from the ignition switch to the fuse box, headlight switch, ect. The red wire connects to the black wire on a double terminal on the ignition switch.
The white wire grounds the dome light ONLY, through the dash sheet metal when the switch is tightened on the dash. No other ground is needed. The instrument lights are grounded to the dash.
The dark green wire gets power through the rheostat on the light switch when it's on, from the orange power wire. The dark green wire goes to the 3 amp "inst lamp" fuse and then to all the dash lights on a gray wire. The gray wires are spliced together in the harness to go to all the dash lights.
In conclusion, the light switch has 2 power sources. The red wire supplies power to the switch to a thermal circuit breaker in the switch. In the first position power goes through the internal breaker to the front parking lights. In the 2nd position, it provides power to the headlights through the breaker. The front parking lights go out in the 2nd position. The orange wire provides power to the switch (through a fuse on the panel) along with the glove light, clock, dome light, and stop light switch. When in the 1st or 2nd position, the switch provides power to the tail lights and to the rheostat.
Here are the wiring diagrams:
Here is a picture of your headlight switch:
Here is a picture of your dimmer switch: