The spin function in an old Kenmore belt drive washer is handled by a
number of components, but I am going to gess that your problem is with
one of the three wires going down to the electromagent (wigwag) on the
gearcase.

Remove the two 5/16" screws to the lower back panel, and remove the
panel. Tilt or move the washer so you can look at the gearcase. The
wigwag has the red, yellow, and white wires leading to it. Look
carefully for a wire that is starting to break. Gently tug on the
wires to see if one is about to snap. If you identify a broken wire,
splice in a new one, but make the connection away from where the wigwag
is, because there is too much movement in that area to make a splice
hold.