Stock diff breathers - how d'you know they're working correctly?

They are a valve, but in reality it is cheap and nasty. In essence it is a light spring keeping a soft plastic disc in contact with a tube. As pressure builds up inside the diff. housing, the disc is lifted off the tube and excess pressure is released. When you stop and the pressure drops, the spring pushes the disc down onto the tube. The problem is that the disc is probably open when you go through deep water and the water will pass the open disc and flood into the housing. Most deep fords are usually short in length so the cold of the water will not have enough time to cool the diff. and lower the pressure to allow the spring to close the valve. Plus, over time, crap gets inside the outer tube and the seal is ruined and the thin steel of the spring is destroyed by corrosion.

Roger

For some reason mine do what they should, or as Roger say only short bath so not cooled enough to suck the water in.
Have never seen gray oil with signs of water when servicing my driven cars with water level on the bonnet.

But I have had parts cars with Grey sludge in diff and transfer.

If you are going through water any deeper than the bottom of your wheels on anything like a regular basis you really want extended axle and transmission breathers, a kit and the time taken to fit it is much cheaper than fixing a damaged drive train.

Oh no doubt about that Lambert, Just thinking how strange it is that I never had any mishaps yet.
Never intend or plan to dive either but then it just happens 1000km from home.
Got hoses and everything ready too, just needs to get done.

Transmission cases on my car have original breather hoses up to a higher point on the fire wall.

Make your own for around 15 quid
1/8  BSP tap 
1/8 elbow to 6mm push fit pneumatic connector
6mm outside diameter pneumatic pipe  all parts available on eBay
Pop of original breather cap pull out spring then tap the hole