wow, then it might be some kind of factory shifter. I had a Pontiac 4 speed with a factory shifter and it mounted on the passenger side of the tailhousing. It was the only one I'd ever seen like that, and it did mount the shifter right in the middle. Here's a very poor photo taken off a video tape. It would be interesting to know if your shifter looks something like this:
The linkage on this unit was very tight, but the shifter head and handle connection was really sloppy.