As a former rear-axle specialist for Toyota I can add this comment:
The automotive differentials are especially sensitive to generating noise and the hydraulic brake lines will conduct that noise to the brake master cylinder which is mounted on the firewall which, in turn, is a wonderful sound-box.
"Noise" (Toyota Rear Axle School at Gulf States Toyota) is defined as "objectionable sound". It was and is horrible in a typical vehicle if the ring/pinion do not run silently. The tooth/heel/depth the ring/pinion gears face can generator quite a noise if not finely adjusted, and the family auto is a closed compartment surrounded by structure that conduct that sound. We spent many hours in training to learn how to adjust/shim/pre-load those gears and bearings.
This is unlikely to be a problem in a tractor, as you might imagine. Sooo***8230; simply make certain the gears mesh within their center orbits of their gear teeth. A good way to do this is use Prussian-blue smeared on the faces of the teeth and rotate the assembled gears while still on the bench. Then you can use the shims (and any bearing pre-load) to adjust the pinion depth so the Prussian-blue wear pattern centers on the gear teeth...and you're good to go.
Now close up the unit, add the gear oil and reinstall.
Hope this helps.
