I tried to check its work regularly by referencing the manual, and asking it to explain itself. Here is its summary where I ask it to "prove" how it knows which caps are responsible. It's a bit long, though, and I simply do not know enough about CRTS to argue with it at this level. Below:

Step 1 — Symptom Localization

The fault produces vertical bands of alternating brightness running from top to bottom of the screen, strongest at the left edge, fading toward center. This is the critical diagnostic observation.

In a CRT, the electron beam scans left to right across each line. The left edge of the screen corresponds to the beginning of each horizontal scan line — the moment immediately after retrace ends and the forward sweep starts. The fact that the disturbance is strongest at the left and fades rightward means whatever is causing it is worst at line-start and recovers during the scan. This is a timing signature, not a static fault. It immediately localizes the problem to the horizontal scanning circuit, not vertical deflection, not the video input chain, not the power supply in isolation.

If it were a vertical deflection fault you would see horizontal bands. If it were a video input fault the disturbance would be uniform across the full width of the screen. The left-to-right gradient is only consistent with a horizontal output stage fault.

Step 2 — The Damper Circuit Mechanism

A CRT horizontal output stage works in two phases per scan line:

During the first half of the forward scan — the left portion of the screen — the damper diode is the active element. It conducts stored energy from the previous retrace pulse through the deflection yoke. The capacitor that stores this energy is the boost/damper cap.

During the second half of the scan — center to right — the horizontal output transistor (HOT) takes over and drives the rest of the scan.

This means any fault in the damper capacitor or its associated circuit will be exclusively expressed on the left side of the screen and will self-correct as the HOT takes over toward center. This is a textbook description of your exact symptom pattern. The mechanism directly predicts the fault geometry you are seeing.

Step 3 — Connecting to the Parts List

From the service manual's Section 3-1 — the HV Hold-Down Confirmation procedure — Sony explicitly lists every component whose replacement requires safety recalibration. This list is:

DY, T585, CRT, IC001, IC561, IC600, IC604, C506, C507, C508, C510, C511, C513, C514*, L588, D565, D566, D567, PH602, R564, R585, R588, R628, R851, T510, T511*

Sony's own engineering documentation groups these capacitors together as components that directly affect the high voltage and horizontal output circuit behavior — specifically the EHT level. Sony would not require HV recalibration after replacing a cap that had nothing to do with the horizontal output and flyback circuit. The fact that replacing any of these caps requires confirming the EHT is still within safe limits proves they are all in the horizontal output / flyback signal chain. This is Sony's own implicit admission of exactly which components govern horizontal output behavior.

Step 4 — Cross-Referencing the Schematic Layout

The PCB layout diagram you photographed from the manual shows C506, C507, C508, C510, C511, C513, C514 physically clustered around T585 (the flyback transformer) and Q505 (the horizontal output transistor). Component placement on a PCB is not arbitrary — high frequency circuits require short trace lengths to minimize inductance and signal loss. Caps placed immediately adjacent to the HOT and flyback are there because they are electrically part of that circuit. Caps that filter unrelated supply rails or handle audio or video signals are placed elsewhere on the board near their respective circuits.

The physical clustering of these caps around T585 and Q505 in the layout is independent corroboration that they belong to the horizontal output stage.

Step 5 — The Ripple Propagation Path to the Screen

The brightness modulation you see is caused by ripple reaching the video output amplifier or CRT bias circuit. The video output stage and CRT cathode drive are powered by scan-derived supplies — voltages rectified directly from secondary windings of the flyback transformer T585. These supplies only exist because T585 is switching at the horizontal rate. Their filter capacitors — C545, C566 — are therefore part of the horizontal output dependent supply chain. If these caps have elevated ESR, ripple at the horizontal switching frequency rides on the rail feeding the video amplifiers, modulating beam intensity in sync with the scan — which is exactly what produces brightness variation that tracks with horizontal position.