Mrmiata,

the birdcage is comprised of the A pillars, the T top and the B pillars .

Also check the vacuum operated headlights and wiper door. The vacuum system can be costly if it's not working with parts missing. Ask for original doc's like build sheet or tank sheet, bill of sale, maintenance records. These would add to the value as well as a matching engine.
Inspect it before it is painted. Check the bonding stripes that hold the fiberglass together, top of fenders and 1/4's.

also go to the forum.