There isn't a second wire on the foot stomper style, exept for the one that bypasses the ballast resistor. The switch in this case only contacts with the starter itself, directly to the armature. Just from the sound of what you describe, is may have a dead spot in the armature itself. One way to test it is to tap the starter housing lightly with a ballpeen hammer while someone cranks it over. Sometimes they just hang up. If it doesn't go, then it's time for an overhaul.
