Originally Posted by ctmccloskey

Like Kanvasman suggested it is most likely a "ground" related issue that is plaguing your Corvette's rear lights. I would start in back and verify that you have a good ground connection to the tail lights. Since it affecting several lights it might be a branch connection in the ground system for the rear of the car.

I cleaned the sockets with DeOxIt electrical connection cleaner and the tail lights became "slightly" brighter after the terminals were cleaned in the sockets After 58 years of being on the road my C3 tail lights were not getting 100% of the power into them so they put out a little less light. After cleaning one side and checking after dark outdoors, it was plainly obvious which side had been cleaned. Now I clean every light socket I come across as well as any other major electrical connection. DeOxIt removes all corrosion simply wiping it off. If you don't have an DeOxIt (available on Amazon) you could use a #2 pencil's eraser and gently erase the oxidation away. This is a gentle way to clean the connection or socket.

On one instance we had a Forum member who used Die-Electric grease on the bulbs and then had problems. Die-Electric Grease IS NOT CONDUCTIVE and if it is used in between the bulb and the socket the bulb will not light up properly because the grease blocks the power. The same goes for Spark Plug wires where somebody puts it inside the Spark plug wires cap and the engine starts missing on that cylinder. One guy used it on every battery connection, kind of strange that he had issues right away...

Die Electric grease is used to lubricate the inside edge of the spark plug boot to keep the boot from sticking to the spark plug's porcelain and potentially breaking the spark plug wire when it is pulled on or being removed.

This is another place that a tool called a Power Probe could really make the job MUCH easier. The P.P. 4 has an LCD screen which reads out the voltage at the connection you are touching the tip to. If you want 12 Vdc at the tip you roll the rocker switch one direction, If you need a ground you simply roll the switch the other way and you will have (0 Vdc). The tool uses the battery power to operate and has been one of the best tools I have for working on the electrical system. I used it on my C4 as well, the fuel pump was not running but I was able to quickly find that with full power the fuel pump ran fine. Then you go to the next connection and follow the voltage drop until you find it's source. On my C3 I was able to start at the window motor that was not working, after applying 12 Vdc to the motor directly at the harness connection I was able to see the motor worked fine when powered up which meant that was not the issue. This tool is awesome, I just wish they were less expensive so more people could enjoy all the benefits of having and using one.

P.S.
If reading a schematic is hard then you might consider getting in touch with DocRebuild who sells a nice set of laminated Wiring Guides showing the path of the power which is a bit different than a schematic. He also sold me a chart that shows all the connectors used in the Corvette so you can identify a connector and know where it goes. I believe they are called the oSoEZ wiring guides for 1958-1977 Corvettes