Tail light works but not brake light

My brake light is not working properly. When
I have my lights turned on, both tail lights
work. When I push in the brakes, however,
the passenger side does not get any brighter.
If the lights are not turned on and I push on
the brakes, the same light does not turn on at
all. I changed the bulb and I still have the
problem. The brake light fuse is also fine.
One thing is that the socket that the bulb
goes in looks sort of burned or blacked. How
do I know what to fix? Should I replace the
whole socket piece? Thanks!