The board in that thread looks similar to yours. However, your loose wire seems to connect to the multi-position Mode switch ( ? ), and in that other thread the switch had been replaced so the wire colours differ.
The wire ( is it green or yellow ? ) seems to have a long soldered tip, as though it has been unsoldered from the PCB rather than broken off. Do you see any "empty" holes on the board, or joints with disturbed solder?
It looks like the wire goes to the back of the mode switch but it's difficult to see, any chance of a close up picture of the back to the switch? Just follow the wire and take a closer picture of where the other end of the wire goes
can you see any number or model in the pcb card? it can be easier to solve the problem that way.
For a fast look at the picture i guess that the upper pod is the wire speed has it goes directly to the pcb and the lower one (middle) must be the spot welder timer as it goes to the step transformer dial.