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This is caused by a bearing in the gearbox. Probably a layshaft bearing.
The reasons for this diagnosis is this.
When you have the engine running and press the clutch then the first motion shaft slows down or stops if held down long enough.
The lay shaft is also used to drive through every gear except 4th which is straight through from the first motion shaft to the main shaft. Although the layshaft will still turn it will not be under load which is why it quietens down.
The quick fix is to replace the gearbox as it means buying a secondhand one and just fitting it rather than removing the gearbox, stripping it down, replacing the bearings and any other worn parts, rebuilding it then refitting it.
I would also recommend you replace the clutch assembly at the same time although it does add to the expense.