Unfortunately dielectric grease is not conductive. So adding the grease might have made the problem a bit worse.
One thing to be aware of is that it is possible to have 12.2 volts at the socket. But high resistance might stop any amperage from getting through. You might benefit from a 12 volt test light that will tell you if the current is enough to light a light.
Amazon If the test light shows the socket good then either find a way to bend the prongs in the socket; Or just replace the socket, available online or at the parts house.
Socket If the test light won't light then you're going to have to trace the harness and check for light at every connector you find. If it gets to be too much or too expensive you could always tap into the working light and run a power wire to the non functioning light.
Harness
