The keyboard wasn't working due to damage to the membrane near both ends of the connectors. I initially tried cutting away the damaged areas, but that didn't help due to the poor condition of the conductive tracks. So I bought some conductive silver-based paint and repaired them:

This helped, and now the keyboard worked, except for two keys, "B" and "N," as far as I remember. It turned out that the conductive track inside the membrane was damaged, and it seemed impossible to repair... But I tried it anyway:

It took me a few days because silver paint needs at least 24 hours to dry.

Finally I got it to work:

However, I then discovered a newly-produced membrane on a German website:

This is certainly much better than 40-years old, of course:

All that was left to do was clean the rubber keys with isopropyl alcohol: