How do you know that the connector is the problem? Do you have any pictures? If you have confirmed that the connector is the issue, your cheapest alternative is to cut the damaged connector, splice the wires and connect the used connector. Make sure to isolate the connections properly. The other option is to replace the headlight wire harness but that would be too expensive of a repair.
As far as the fuel gauge I don't think they are related. What makes you think the two issues are related?