[DavGoodlin]

If you have the scrolling sideways, it often means the sync pulse is getting interrupted. This drove me batty with a set I had in high school, long ago.

It happened on a 1965 RCA color set chassis CTC16XL, and I replaced several tubes then horizontal AFC diodes (described by Davewm) with no improvement.
Then, with no outside advice, I replaced the HV rectifier tube which WAS a newer Sylvania 3CU3 with a new-old-stock 3A3 and the picture locked solid like never before. My conclusion is that the 3CU3 was shorter and did not seat fully into the flyback as RCAs do.

So, your problem could be some very mild and intermittent arcing, possibly at the HV rect tube or tripler block, if this set has one instead of a tube. Either way, its on the AC side, not the DC side after the rectifier/tripler that goes to the picture tube anode.

Keep the back cover off, HV cage open and when the picture "goes flopsy" turn off all the lights and look for some purple glow along the lead from the HO tube, into and around the flyback and HV rect tube. Clean up and RTV silicone the area that is arcing.