I checked all the fuses in the engine fuse box, and all were fine. I bought a wiring diagram and Mitsubishi calls this engine fuse box the "PDC or power distribution center".
From the wiring diagrams it looks like the headlight circuit is double fused. That is, one fuse for the circuit from the switch to the headlight relay and a larger fuse on the high amperage side of the headlight circuit.
I burned out the light switch in the steering column by putting the wire across the headlight relay. I can't figure out why that happened. Seems like I would have blown the fuse before the switch was damaged.
The Mitsubishi dealer said that they don't sell just the headlight switch. The whole electronic assembly in the steering column must be replaced and the part costs $289.
I wasn't going to spend $289 for a switch for a 16 year old car. I went to Checker auto parts and picked up 2 $5 switches (one for the tail lights, one for headlights) and wired them in.
I passed the safety inspection for another year with a little bubble gum and duct tape!
Side note: When they did my emissions testing, it got an excellent emissions score. Not bad for a car with 137K miles.