Why is cigarette lighter not working in 2003 mitsubishi eclipse?

Try the easiest and cheapest idea first (check for a bad fuse). I think that you already tried that. You could also interchange the hot temperature part of the cigarette lighter for another lighter from another car (they are all interchangeable). You don't need to change the wiring to do that, you just unplug the old part and plug in the replacement part. If you are still puzzled, you could stick the probes of a volt meter (or probes of a 12 volt light) in the cigarette lighter to see if you get voltage. You might have a broken wire to the cigarette lighter, and that would require you to trace where the wire gets voltage and where it does not.

The lighter has a fusible link wire that is built into the bottom of the unit. With constant use of phone chargers that don't fit exactly in the socket you either blow the fuse or burn that wire out. I just pull the lighter and replace the wire with a regular 20 awg wire. If you pull the lighter out, check for B+ at the wire going to the center of the unit, not the ground on the side of the housing. If there is power there the wires probably bad.

Has to be the another fuse.