Right - all '71-'73s are floor-mounted shifters.
Do you have a tilt, or non-tilt column? There is a difference between the two, and there are two different signal switches offered depending on which one you have.
As for the possible 'column shifter' issue, as you put it: there is a collar on the column that has a connector to transmission linkage at the firewall end of the column. That works with the shifter to prevent either the steering wheel or the key cylinder from turning [to start or stop the engine, I imagine] while in anything except Park.
Yes, there is also a neutral safety switch that prevents the car from electrically starting specifically when it's in anything except Park and Neutral, however, this collar/linkage device physically blocks either the steering wheel or key cylinder from turning (I don't remember which one, for certain - it's been a few years since I noticed this 'feature').
Mine is not currently connected and the linkage has been removed, so I have it permanently positioned to allow the wheel or key cylinder to turn. I discovered this while rebuilding the column, and happened to notice the "lock-up" feature by observing the position of the linkage connector on the firewall end of the column.
I'm sure there's a better, more exact answer explaining the actual function of that device... I'd be interested to hear it myself, actually.