1965 Dodge Dart GT convertible with 318 and 727 Transmission, linkage or cables do not work.

'65 and earlier transmissions were cable-controlled. '66 and later used a mechanical linkage. It sounds like you've got a conglomeration of parts that weren't meant to work together.
Either you've got an aftermarket shifter in your future, or you will need an adapter kit like this one offered by Imperial Services that will allow you to retain your factory console and shifter:
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Imperial Services - '60-'76 A-Body Parts