The noise that David is referring to is very distinctive and very recognizable by those that have heard it before. It sounds rather like and can be confused with, by the uninitiated, a bad ball bearing race. You can get a good idea if its the Reverse Idler Gear using a mechanic’s stethoscope to find if the noise is emanating from the Right Rear corner of the Gearbox.
The ultimate test is with the Gearbox stripped and with the Lay Shaft Cluster and First Motion Shaft reinstalled (the Reverse Idler Gear still in place). Drive the First Motion Shaft with a Hand Drill, taking care not to damage the First Motion Shaft journal that engages with the Flywheel Centre Bush; I use a short piece of hose clamped to the First Motion Shaft and drive it via a short piece of steel rod clamped in the other end of the hose.
Spinning the First Motion Shaft and therefore, driving the Lay Cluster simulates the clutch being engaged and with the Main Shaft removed, noise from the other gears in mesh with the Lay Cluster is eliminated. Because there is no Reverse Gear in the Gearbox at this point, the Reverse Idler Gear can be freely moved to the rear, where it would be when engaged with Reverse Gear, and to the front, where it resides when Neutral, or a Forward Gear is selected, whilst the Lay Cluster is spinning.
If the Reverse Idler Gear is the issue, you will hear a distinct change of sound when the Reverse Idler Gear is moved from the Front (Neutral - Forward Gear position) to the Rear where it is when engaged with Reverse Gear. If the problem is not with the Lay Gear Cluster, the noise will disappear when the Reverse Idler Gear is moved to the Reverse Gear position and reoccur when moved back to the Neutral/Forward Gear position.
Invariably, when the Reverse Gear is examined, you will have to look hard to see slight wear on the area of the Gear that would engage with the Reverse Gear. At first glance you would think that there is nothing wrong with the Gear. When the Revers Idler Gear is in the Neutral position, its the rear section of the Gear that engages with Reverse Gear that meshes with the Lay Cluster Gear.
The only practical way to rectify this fault is by replacing the Reverse Idler Gear. Practically every Gearbox I refurbish has noise being caused by the Reverse Idler Gear and as this Gear in new form has been rather hard to locate, I now manufacture my own.