How to route new overdrive harness through gear shifter?

[jeff4912]

My overdrive button on the end of the gear shifter does not work and the wire harness between the overdrive button and the switch connector on the steering column needs to be replaced.

Any trick to this or is it as easy as disconnecting the wires at the overdrive button on the end of the shifter and pulling them out the bottom of the shifter and feeding the new one in from the bottom of the shifter and push it through to the top?

 

[Number4]

Why do you suspect the wiring and not the button?

 

[jeff4912]

Found break in wire at base of shifter, where the wire comes out of the base of the shifter to the top of the steering column.