Dash lights out....not the dimmer switch

Fuse.

You're going to have to break out the meter and find out where your losing your power. Did you test the 'new' switch before you installed it? It could be bad too since no dash lights is the most common fault with these switches.

A diagram for Instrument Illumination can be found at Instrument Lights Wiring Diagram Please... - Mustang Forums at StangNet

If your dimmer is one of the old style aluminum case units then you need to set the meter to a low resistance (ohms) scale and probe across the two silver colored terminals. While holding the probes across the terminals turn the dimmer knob and watch the meter. It should be a fairly smooth increase/decrease in resistance without any 'drop outs' in the reading.
If you have the newer plastic case switch then you probe across terminals R & 1. The identifiers are molded into the case next to each terminal.

To trace for power follow the circuit diagram and check for voltage along the dimmer switch circuit. Take the negative probe and connect it to a metal chassis part/screw and take the red lead and probe the connection points along the circuit. The BR wire behind the main light switch that goes to the back of the dimmer is a good place to start. With the main light switch in the Park position you should have about 12v at both points.

Check your headlight switch.

Im having the same problem but mine works sometimes out of nowhere and the next minute it will go out.