Does the lighter still work? If so, I'd leave it alone until its fuse starts blowing regularly. I removed mine several decades ago since neither I nor Judy ever smoked, so its only use to us was a complicated and untidy way to power a radar detector or CB radio. Direct wiring made even that unnecessary.
If you can get it out of the console, try sticking the whole thing without disassembly in a sonic washer for awhile, then let it dry for a few days before trying it out- direct-wired to a spare battery. The exposed heater coil in the base builds oxidation just like your breakfast toaster does.