Ethan Dicks Says:
"...Considering you have both that wide shimmy and the horizontal roll, I'd be looking at more than one failure.
Look around the vertical hold circuit - check for potentiometers - they could be dirty or have a bad solder joint.
As for the wide shimmy, check the PSU for ripple - the input is ~18VAC IIRC, from the transformer, but locally, the CRT board has a simple linear regulator to +12VDC. The caps right there by the connector are ones I'd look at. Also check the ripple at the large eletrolytic in the base to ensure that's not complicating things with noise/ripple. ..."
NEXT - results of testing...
I think I have a spare good 23000 uF 15v cap, we can start with the big cap near the transformer.