Looking around for a convert and a few sellers indicated that the bird cage is in excellent cond.

The birdcage(cab frame) is the structural core of the body that provides strength and dimensional accuracy, a welded steel skeleton. Corvette Enthusiast Mag. has a good article on the birdcages in the Oct. issue. I know there are issues with rust of the birdcage. The article stated that the anti-corrosion used phosphated steel , coated with green zinc chromate primer was considered state of the art at the time. It was used in aircraft construction also. The designers never thought the cars would still be on the road 45 years later after being exposed to salted roads and being parked outside in the rain and snow. It is expensive to fix. Alot of what I wrote is taken from the birdcage article.

Jon is spot on in his post.  Here are some additional pics.

Birdcage
  This one has firewall and rear panels installed.  Convertible cages similiar, but without the t-top support.