You really need to check if it's wiring or the connector. Even just a random car bulb with some wires will do.
I'd start by getting that panel off (think you have to remove the trim around the gear levers and working up), then get the wires off the connector, hook your bulb or voltmeter to them (doesn't matter which way round). If the bulb lights it's the connector and you can get a new one from a spares site.
If it's the connections then it will either need:
- working back through the loom connections to find the broken wire, or
- simply safely abandoning the connections and run new ones splicing into the working cigar plug's wiring.
Remember that the right hand one has an additional connection near its face for illumination you can safely ignore.