Before unwinding it, I'd remove the cover and see if one of the wires didn't
get soldered properly to the pin. With thecthin enameled wire used in such
transformers, it isn't uncommon for the insulation not to get removed
properly to make a good joint. A good magnifier will help.
If you need to rewind it, make a careful count of the turns, as one side of
T2 is the VFO coil, and the value will affect the tuning range. Hopefully
the break is in the output link side and doesn't require removing the
other winding.