The power pack is up behind the pushbuttons and very hard to see. But it's there if ever your lights were working.
I is it all lights that go out, or just the electroluminescent dash gauges?
If the bulbs in the pushbuttons stay lit, it's probably the power pack. If all lights (including standard bulbs) go out, then it's probably the switch, most likely the dimmer portion that you rotate to set the brighness of the dash lights. You might even get them to come on intermittently by trying to twist the dimmer back and forth to reconnect it temporarily (find a spot that works).