How to repair vintage compute flexi cable?
Fairly easy on Kapton** cables, as long as the tracks are fairly wide and spaced. If it is fine, you need a fine tip, and magnifiers or binocular microscope if you have it.

Use a scalpel with a curved blade, with the blade perpendicular to the surface to scrape (abrade, not chisel) the Kapton coverlay off the conductors either side of the break. You should scrape off an 8mm length. Scrape to bright copper.

Using fine tin-lead solder, tin the tracks the whole exposed area.

Cut a 3" length, and strip 1/2" of insulation off the end of some wire wrap wire - it is silver plated and very nice to solder with. Tin 10mm of the end.
Sweat it down onto the track at one end with the soldering iron, then the other end. Then cut off the wire carefully with the scalpel.

After repair it will be electrically good, but it can't be allowed to flex  in the repaired region as it will fail.

Cover and reinforce an area wider than the repair with Kapton tape, hotmelt, flowable silicon or something else suitable.

**Orange/goldy Kapton doesn't melt under soldering iron heat. White PVC flat cables can be nightmare as the totally melt.