@Hershey & Chris - As I mentioned, that car was given to me by a friend and had sat unused for several years exposed to the harsh winters of northern New York state on her farm. When the the mysterious raising and lowering of the driver's seat occurred, I was absolutely stymied until I got out of the car and looked underneath. The floor of the car had rusted out, and the rear end of one of the seat rails (ie, that the seat rides back and forth on for adjustment) dropped down and touched the ground. So, when I started to back out of the parking place, it jammed into the ground and essentially tried to pole vault the seat into the air. In contrast, when I went forward, the seat went down, and the back end of the seat rail then just dragged on the ground. The problem had absolutely nothing to do with the suspension, LOL.
Over the years, I've probably asked 100 or more friends, car enthusiasts, and professional mechanics if they could come up with an explanation for the strange behavior, and only one guy, an old mechanic, knew what probably caused it, and that was only because years before, it happened to one of his clients and it stood out in his mind.
Cheers,
Tom