Here are some of the waveforms I got with the picture locked.
Sync phase inverter (12SN7, pin 4)
Attachment 194193
Horiz, AFC (6SN7, pin )
Attachment 194194
Horiz, multivibrator (6SN7, pin 6)
Attachment 194195
After I got these I tried to check the waveform on pin 1 of the oscillator tube.
When I connected the scope probe to that point the lock just disappeared completely.
Is that a clue?
Ignore the 2 dots in the pictures, its a reflection from the ceiling light.

I think I have found the root cause of the problem.
Video noise on the sync signal. When you turn up the contrast there are various points on the right side of the screen that pull to the right. But when the screen is black, it goes away.
I will be doing some more probing with the scope to find where it is coming from.

The video noise appears on the power supply.
It goes away when the video output tube is removed from circuit and connect to the filament string with clip leads.