There's actually no bearings of any type in a caliper. The caliper itself is a machined cast iron housing, with four aluminum pistons riding inside individual bores. The stock seal are a 'lip' or 'garlock' type seal which is used throughout the auto and aviation world and actually work quite well.
The initial issue with the Corvette application is water, salt, dirt, etc.etc. getting into the cast iron bore. The repeated wet/dry cycles of normal operation causes pitting corrosion on the bore. This eventually becomes more than the seal can handle, and an external leak of fluid ensues.
The cure for this is to re-machine the stock caliper, adding a stainless steel sleeve inside the bore. The stock piston and seal is retained. This simple fix solves the corrosion problem more or less permanently, other than simple old age and dried out seals over a 10-20 year time period.
Another unrelated issue is one where the pedal goes 'soft' and remains this way, or returns shortly after repeated bleeding attempts. The 'lip' seals referred to above do an excellent job of sealing the fluid inside the caliper- much better than any other type of seal. What they are not designed to do is resist contamination from outside trying to enter. If there is an external force that frequently pushes the brake pad back into the caliper, it's entirely possible that air, dirt, salt etc, will get pushed inside as well. The result is seal failure and leakage. Stainless steel calipers will not prevent this, as this failure mode has nothing to do with corrosion of the caliper bores.
The fix for seal failure is to convert from a 'lip' seal configuration to an 'o-ring' type. This may or may or may not also requires using different type pistons that are suited to the shape of the o-rings.
The advantage of o-rings is that they seal equally well in either direction, so to a limited degree, the air and dirt pumping problem is solved. The downside of o-rings is that they do not seal as effectively under high pressure as a lip seal, but in a practical sense this is not a concern on a relatively low pressure application like a Corvette brake system.
One issue that frequently gets overlooked is the root cause of the pads 'pumping' dirt and air into the calipers.
Two main causes for that-
1) a worn rear wheel bearing that allow the axle, rotor and wheel ass'y to wobble back and forth causing the pads to be shoved away from the rotor.
2) a warped rotor (very rare) or a replacement rotor that has not been machined after installation to run 'true' on it's axis(very common).
C2 with disk brakes and C3 Corvettes are very different animals when it comes to rotor replacement. They cannot be changed out in the same manner as today's cars where the old one is tossed out and a new slapped on and and away you go.
Odds are that there is sufficient run out with the new rotor that the pads will be pushed back into the caliper even after a short drive. A soft or low pedal is the result and pumping or bleeding is only a temporary solution. O-ring calipers don't solve the issue, but merely mask it.
The correct solution is to have the new rotor machined in place on the axle and be done with it.
Sorry for the long post.