I have a 1984 Curtis Mathes TV (its the large console 25" i think and it has the stereo, 8 track, cassette, and record player in the top of the cabinet) The screen bounces its a nice picture, but even after running a few hours it still bounces. The screen seems to "bobble" about 1/8 ~ 1/4"

Hello. If tapping on the TV makes the picture jump, it confirms that a defective solder connection is the cause of the jumping picture. I would say that most likely the defective connection is on the pins of the vertical output amp IC. These are both repairable. That said, putting a lot of money into a 1984 model is difficult for me to recommend to you. J.