In addition to cleaning the CRT pins and socket, you might want to try re-soldering the CRT pins.
But be prepared for the worst...I had a similar problem in a 14'" DuMont portable that was caused by a bad weld to the cathode sleeve inside the CRT. The picture was very dim and smeared, in fact that I did not see it at all until I darkened the room. I tapped on the neck of the tube, and the image appeared at full brightness, but was quite intermittent. I tried to "spark weld" the connection, but it did not fix the problem.
jr