Have you checked out the operation of your charging system since the rebuild? How old is the battery? What is the voltage of the battery with nothing drawing power? With the car running what does the battery voltage show?

It could be a dirty or loose connection on the battery or your alternator could be suspect. Sometimes the problem can be caused by corrosion at the little post that supplies the Fusible Links with power. The post is behind the battery, it is attached to a frame rail and has a nut on it with several wires making connection. There is a battery Positive wire that comes back from the battery to supply the power. Each of the connections has a ring terminal and mine were copper or brass and had a ton of corrosion on them. After cleaning this post and all the ring terminals everything electrical was working with full battery voltage. Prior to cleaning the terminals my radio had 11 volts going into it, even the fuse panel gets corroded on these cars.

People used to put "Overdrive" pulleys on Corvettes trying to free up more power, the bad side is that they slow down the alternator and the water pump. A very bad idea on a C4 Corvette.

On the "whining sound", does your car have a power antenna? Is it working as it is supposed to? When they break you frequently get a constantly running antenna motor which makes a bunch of noise, especially at the rear near the drivers side of the car. If the fuel pump was making the noise it would be centered over the gasoline fill cap area.

A freshly rebuilt L98 sounds nice, Mine has 103,000 miles but the compression test showed the engine to be in great shape. These are great cars for cruising around in, I love cruising along at 60 mph getting 30 mpg from my C4 while listening to the CD player The one thing I did change is the radio. I removed the semi-functional Bose Gold Stereo and installed a new modern stereo that connects to my phone when I get into the car, well worth the effort and expense.

I hope that these suggestions might help you in finding the whining noise and solve the dimming problem!

 

Whining noise listening at fuel filler or under rear of car if noise is noticeable fuel pump or pulsator. Pulsator was initially were installed to reduce fuel pump noise. Later pumps were quieter so pulsators aren't necessary. If it original pump might be worthwhile to change it out I would also replace pulsator with a short piece of hose.

Charging System. Check connections, ground cable to block and to body grounds, positive connections at underhood junction block and fuse blocks. A charging system test would be in order. Typically not expensive, some auto parts stores do them for free.

 

Your fuel pump may be making noise because its pulling extra amps to keep up when the voltage drops.

Definitely seems like you have an alternator issue. You could have it tested just about anywhere.