Worked on a pair of those for Hotlead, and it had the exact same problem. However, he never knew that part because he never used the toe brakes. I did fix the broken connections, but it was difficult because the conductors were some alloy, probably made of or at least containing steel, allowing them to be very fine and yet mechanically strong. Ironically that's their downfall because that mechanical strength causes repeated flexing mainly at the connection, where it snaps off. BTW, those wires are not unjacketed. They have a thin layer of clear insulation on them that must be stripped off to make connections. In any case, that metal resists soldering pretty fiercely and it's difficult or nearly impossible to get a molecular bond between the solder and the conductor. In my case, the wires broke at those white connectors on the circuit board. The wires are crimped in the back of the pins in the plastic housings. Those pins can be carefully removed from the connector. I think I re-opened the one that was originally used, brass I think (not an easy task), then re-crimped the newly stripped wire back on, making a good mechanical and electrical connection. I did hit it with some solder at the connection just to make sure it didn't come loose, since the crimp wasn't as good as the original. After that I reinserted the pins back in the connector, and secured the wires in a way that tried to minimize movement at the connections.
It was all a waste of time though, since the REAL problem with his pedals was that it was electronically dead (that little circuit board shown in your picture). I tried to find a replacement by attempting to procure an old set of the same kind of pedals to cannabalize from, but it turned out those pedals were pretty rare and I ended up sending them back to HL as a failed attempt on my part.
At some point he got a set of MFG Crosswinds. I've used them for years without any trouble. Once you see the construction of those expensive brands, the quality is obvious. Do yourself a favor and upgrade. COVID-19 relief stimulus payment is on it's way to you