Isn't there a reinforcement plate on the driver's side under where the antenna goes? Or is that for the outside mirror.
No plate (that I remember) - original style antenna.
http://chevy.oldcarmanualproject.com/radios/51rs/51rs40.htmThere is a mounting bracket near the bottom of the original-style antenna that attaches to lower inside cowl (in some/all A-D years there might already be a hole for the attachment screw).
Non-original design antennas might or might-not have a lower brace/bracket.