Yup, silver ink pens is the way to go for repairing flat flex cables

. Done many over the years without any issues. I have a Roland U-20 I use for a MIDI controller sitting here. About 20 years ago a section of the keyboard stopped responding. Upon opening the keyboard up I found the flat flex cable that ran between the keys and the main board had several burned traces

. Including the collateral damage I think I had to repair 7-8 traces. I picked up a Chemtronics silver ink pen, probably from MCM Electronics back then
Silver Ink Pen @ MCM. I used the pen and painters tape to repair the cable. 20+ years later and it's still working without any issues. But this cable is relatively static and is certainly not seeing any sort of mechanical stresses so that would be more ideal conditions for this sort of repair.
Unfortunately, it appears your situation is less than ideal due to the mechanical aspect. The way I would approach it would to be repair the traces with the pen then overlay the top with PET (that nasty plastic they make clam shell packaging out of) or mylar, carefully dressing all the edges to help protect the ink and see how long it lasts. Also, be aware that there are 2 common types of conductive ink pens: Silver and Nickel bearing. I've always used silver ink so I don't know how nickel compares. It's a lot less expensive and might hold up better mechanically compared to silver.
These mylar/conductive ink keyboards are some of the cheapest, nastiest designs I've seen for a keypad. In the past I've reverse-engineered them and made a replacement using a conventional PCB and Cherry MX switches. They're cheap, reliable, and I can get custom key caps made for them reasonably to boot!
BTW, another really handy use for these pens is repairing automotive window heating grids (rear window defoggers here in the US). I just run down the broken grid line with my DMM set to DCV to find the break, mask it with painters tape, paint over the break with the pen. Rinse and repeat as req.