Detail of the turntable’s ‘OUTS.’ With labeled connection points.

The bottom of the case comes off with just around 13 screws, which appear to be identical, so keeping tracking of their location isn’t necessary.

This is the view of the turntable’s innards, which will greet you after removing the outer cover. In the bottom-right corner you can see the stereo and ground outs, which were protected from view by a little metal cover that has been removed along with the cables.

Here are the old cables, after being pulled away from their connections. The inner wire carries the signal, and the outer shield (often braided copper *see new cables* but in this case seems to be braided aluminum?) is twisted and soldered to ground. Here’s a link to a diagram of an RCA connector:

I used some good quality 6′ RCA cables, which will end up giving me a little more length and better quality than the 25+ year old original cables. These are standard A/V RCA cables, I pulled off the third “video” cable, chopped the connectors off one end, and stripped the insulation back.
Then I neatly twisted the braided copper shield.

As shown in the first detail of the Technics’s output terminals, I identified the correct terminals and soldered the new cable into place. Then, I carefully taped back the delicate wires that carry the signal to the up and through the arm an into the turntable’s cartridge and replaced the protective metal cover, making sure not to pinch the wires. Because of the thicker new wires, I thought I might have to dremel the outer plastic case, but it squeezed on fine.