It sounds like your trans is the 50s-early 60s GM OD. The OD is still Borg Warner. Inside the solenoid there is a big wire soft soldered to a bar that connects to the coil windings.. That solder will melt under too much current hopefully before the windings melt. It can be reattached. It's not a modern fusible link but it could be reconnected with a link wire.
When the cable is pushed in it is "in" overdrive. When the cable is pulled out overdrive is locked "out". On the Stude the cable goes from under the dash through the firewall and loops back to the trans. So when the cable is pushed in the OD lever is pushed back and when the cable is pulled out the lever is moved forward.
