Strange Noise During Acceleration From A Stop On YJ

Here's one that's been bugging me for at least a year. After I've been
on the road for a few miles and the Jeep has warmed up, when I pull out
from an intersection, I hear a whirring sound (like a spinning bearing),
which goes away as soon as I develop a little speed (like after
completing a left turn after a stop at an intersection). As long as
it's making the noise, if I let off of the pedal right away, it stops,
and when I accelerate again, it kicks back in, at least until I exceed
some threshhold of speed or rpms. I thought it might be the fan clutch,
but the clutch is fine. I thought that it might be the bearing in my
alternator, but the alternator has been working fine ever since the
Wrangler developed this annoying sound a year ago. It's annoying, kind
of like the old Toyota Previa mommy vans from the 90s as they pass you
on the freeway, making their "deer whistle" sound (the whirring,
whistling sound that I imagine scares deer out from your path with one
of those questionable safety accessories from the JC Whitney catalog).
As soon as the YJ either shifts, hits a certain speed, or rpms (after
being at a dead stop, like in bumper to bumper traffic, or traffic
lights), it suddenly goes away. To make matters worse, it's
intermittent (hard to reproduce reliably, like in front of a mechanic).
My mechanic (who finally heard it last week) suggested that it *might*
be the water pump bearing, but he doesn't think so, because there is no
weep, no loss of coolant, and this has been going on for more than a
year. Any guidance here is appreciated. Pertinent info: 93 YJ, 4.0L
auto, 4.11 gears, 32" rubber, 177K miles, Mopar water pump has about 60K
miles on it.

Regards,

Doug Gavilanes
Garden Grove, CA.