This video seems to show a multi winding transformer connecting to J605. It is hard to read in the video, but I think that is the label near the connector.
While he does open the scope up the video, there is not enough info shown to know the voltages needed.
You could try leaving a comment on the video to see if he still has the scope and can measure the voltages (video is 10 years old...).
You you could also trace the circuits near J605 to see what the voltage rails seem to be - i.e. rectifiers and regulators.
I did seem to see a 6.3V label on the transformer, so at least one of the windings would be 6.3V AC - very common in older gear.
Actually, I found a schematic here for that series of scope:
https://elektrotanya.com/gw-instek_gos-620_gos-630.pdf/download.htmlIt shows the windings and wire colors on page 11, but doesn't call out all the voltages. You can likely work them out (from the labelled rectified & regulated PSU outputs), but note that some are high voltages so you need to be careful.
If you don't have a suitable transformer, then this is probably scrap as it would not be worth spending much money getting it working.
Maybe your best bet is to try find a faulty one selling cheap that may have a good transformer.