When you click on links to various merchants on this site and make a purchase, this can result in this site earning a commission. Affiliate programs and affiliations include, but are not limited to, the eBay Partner Network.
The silver part looks like an adapter for an aftermarket ****. The black cup just below that is probably part of it. What year are you working on? There were several changes thru the run of 4+3 cars. When the OD unit failed on mine i swapped in a T56 from a '95 Z28, others have put in ZF6s and T5s and if your budget allows, there are some aftermarket 5 & 6 speeds out there. A T56 swap will need (in my opinion) about a 3.45 or 3.73 rear gear swap.
Typically there can be issues with one of the main bearings in the OD unit. This site is a good place to start. https://www.5speeds.com/dne.htm
These things like fresh oil so if you haven't already, good idea to change the fluid and filter in the OD part of the trans. The OD portion is separate from the trans and uses ATF. Lots of good threads on that here.
Regarding the first pic, I agree, it looks like that's an adapter for an aftermarket ****. Zip Corvette carries replacement stock ***** as well as others. There were two types depending on the year yours is from. The early ones were just a **** and the later ones had the OD button incorporated into the ****.