Is the rebuilt column from the same year as your car? In my experience the cruise control wiring is separate from the the signal switch harness. I added cruise control to my 1970 Dart from a 76 or 77 Aspen years ago, but recall that the wiring was a stand alone harness. I suggest verifying that both your columns are the same vintage as there were some changes over the lifespan of these cars. I ran into something similar when putting a 73 or 74 column into my 75 Dart Sport where there was some slight differences in the harnesses.
You should be able to get wiring diagrams for your 73 from
MyMopar.com, I believe 73 is the latest year available there.