Removal of manual transmission cable to get to reverse switch

[KTS]

I think it's just an open/close switch. Doesn't matter the polarity.
First you will have to remove the cutter pin that connects the cable to the lever, then use a pliers and a screw driver to remove the lock that attaches the cable to the bracket. Those locks are difficult to remove at times. Or you could just unbolt the entire bracket.
Have you tried doing the wiring from below the car? Last time I had to extend the reverse switch wire it was much easier to do from below the car.

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