I have the same problem with my ES. I have only 121000 miles on the car. Last year I picked up a barn dweller that only had 46000 miles on the clock when parked in 1978. I enthusiasticly changed rear end(the po of the barn car didn't recal that the rear end whined when he parked it so long ago) to find that the"new" rear end was just as loud. Since then I have read that most 1800's had noisy rears. If you find a solution please let me know, this is the only complaint I have with an otherwise splendid automobile.

Merci

Yvan

PS any one know of a good rear end shop in Quebec, up-state NY, or Maine?
--
65 122s/73 1800es/80 262c(350ci v8)/81 242na/89 745t/87 780/89 740/89 740t/ 86 745 and too many parts cars and projects to list

The noise you describe is quite probably a symptom of large gear lash caused by wearing bearings in the pinion or large lash in the initial set-up. Listen carefully and drain/change the oil frequently. Budget for a rebuild by a good shop.
Should one of your oil changes reveal metal bits, the whine increases in pitch, the rear end feels "heavy", a vibration develops or a grumble or growl starts then park the car until the rear end can be rebuilt.

The good news is that many rear ends have a whine seemingly forever. The bad news is that some go from bad to worse seemingly overnight. Unless you are racing, you can probably just "keep an ear on it" until something goes worse.

The noise can be other things (axle bearing, loose brake/hub (although that is typically rhythmic and more of a rubbing noise), or the gearbox).

Monitor the oil!

Mike!