I think that the upper potentiometer on the front panel is a spot weld timer, which controls an automatic weld duration time from 0.2 to 2.5 seconds. The part shown, with the two blue wires, is the enabling switch for this timer, which has become detached from the rear of the potentiometer. The metal can and the switch should be attached to the back of the front-panel pot using those metal tabs.
As for burnback, that is varied from 0.02 to 0.25 seconds by a potentiometer on the control board. There is a square blue trimpot on the PCB, with a white slotted shaft for screwdriver adjustment.