it is most likely not working due to a blown fuse
you simply repair it by buying another lighter
http://www.innerauto.com/browse/year/1995/2001/mitsubishi/eclipse/repair_manual/?ref=S1161368748W453914ac6fba6&label=95-98+99+00+01+Mitsubishi+Eclipse+Repair+Manual
One could sell Mitsubishi Eclipse parts on online websites such as eBay or Amazon. As well as this, one may sell Mistubishi Eclipse parts to car repair companies.
Replace: Fuse Socket Element
Also you need to be sure the fuse is working in your car before replacing the lighter.
If its a Ford you have, click on "Ford repair site" under "Related links" below.
buy this book. http://www.innerauto.com/browse/year/1995/2001/mitsubishi/eclipse/repair_manual/?ref=S1161368748W453914ac6fba6&label=95-98+99+00+01+Mitsubishi+Eclipse+Repair+Manual
As far as I know, just pull out the cigarette lighter and you have a 12 volt D/C power source. If you want an A/C (alternating current) power source, you have to buy a convertor to plug into the cigarette lighter socket and then plug your item into the convertor.
Replace the blown fuse, or repair the broken wire.
If you go to autozone.com you can view repair guides online free.
I am going to help you where no one did for me this is the actual factory service manual your local dealer uses in the repair shop it will answer anything you would want to know. http://www.onlinefreeebooks.net/automotive-machinery-power-equipment-ebooks/mitsubishi/2000-2002-mitsubishi-eclipse-eclipse-spyder-service-manual-pdf.html
According to "Haynes Service and Repair Manual" is it Fuse 33 (F33/15Amp).