Low whining sound from undercarriage

[ZR11974]

Good morning to all. I hope this email finds everyone well.
I am a new ZR-1 owner and am hoping I can draw on the vast knowledge, here.
The car is a white 1990. It only has 30K on it and is in excellent condition. I love the car. Lifelong goal achieved by getting the legendary LT5 underfoot.
However, I am experiencing a low whining/whirring type sound from under the car. It does not seem to be changing the cars performance. It's just a concerning sound, and it's loud.
It does not appear to be exhaust.
It is not throwing any warnings, and none of the battery, oil pressure/temp, or normal temp gauges are effected by it. Neither is the idle. It sounds like it might be a belt. But, it starts and ends while moving or sitting still, and it never continues once I accelerate. And, as best as I can tell it appears to be coming from the front/center of the car, not the rear.
Steering also doesn't seem to be related.
I keep trying to isolate some consistency with it, but no luck so far.
And, as I've said, it is loud. Almost like a smaller engine is revving, but not the LT5.
Since it comes and goes with clutch release and depression...sometimes...clutch is my gut feeling.
Any troubleshooting suggestions? I have considered buying a code reader, or using a paperclip trick I read about to see what is stored on the ECM.
I absolutely adore the car, and this weird *** sound is the only thing I'm concerned about.
Thanks for taking the time to read all this, and I hope the day treats you all well.

Respectfully,
Geoff