Dealt with a lot of Trinitron and Sony TVs in the past.
You do not quote a model number, perhaps I have the service manual for it. They are easy to find now.
The fact the "video 1" also shows the smearing and edges could absolve lots of the upstream baseband circuits.
As mentioned above, electrolytics were a common issue, but also bad solder joints on the video and crt boards. While turned on, a quick test "percussion maintenance" could give a hint.
(A few taps and punches, don't go ape on it....) If these changes the traces it is vibration sensitive. Contacts.
Second point is temperature and contacts. (Be very aware the CRT will retain a HV charge) Remove connectors and reinsert inside. A dash of contact cleaner may be useful here as you do that. When you get close to the offending board a few spay of "super cold" will be useful.
Other suggestion for Sony's is a small wooden stick to apply pressure and slightly bend the pc boards white the TV is on. This related to bad solder joints and intermittent traces.
Good luck with it.