Disco 2 Breather Plastic Tubes

Best to all !
2002 Discovery
After a week of research Codes 1171_ which is a small vacuum leak; follow with codes P0135 and P0155. I found the three hard breather plastic-tubing on the right bank of the engine firewall. The gear box tube and the transfer case tube I found correctly connected, but a third tube is completely loose not connected and lost its place on the tube loom-separator. I can not find where it goes. I Looked on the carbon canister, but all the corresponding hoses are there. No luck. I looked in Rave and on the internet, but with no success I couldn’t find any information on the third tube-plastic hose at all. Where does it go ?

Hoping to hear from someone that knows where it goes.

Staying humble, hopeful and very thankful.

Thank you for your time and help in advance.

The odd breather pipe could possibly be the front axle case breather. If it is, then it should connect to a hole on the top of the axle case about half way between the diff case and the left hand side hub (your driver's side, 'cos you lot drives on the wrong side of the road )
It's difficult to offer any help with fault codes without knowing whether the Disco is diesel or petrol (gasoline to you, but not gas 'cos that's something totally different) and what code reader you used.
Oh, yeah, a gaiter ain't the sort of things that swims around eatin' people!
Ahh! Two nations separated by a common language.

Thanks a lot Brian for your quick response. My Roovering Disco is a 2002 Petrol. Just finished putting new head gaskets. Heads were machined.When I bolted them I lowered the engine to have better access to the back bolts,so I when ahead and change the motor mounts new. Honed the cylinders. All the top was replaced. Cleaned the injectors.New timing chain. New oil pump kit. New brass water pump, Power steering pump.Radiator.Plugs and 8mm wires. Air filter and belt. I'm probably forgetting something ! And can you imagine that I can not find where this silly plastic tube goes into ! ;>) I'm raising all of them to the snorkel I'm adding to my monster.
I already found The Front and Back Axles Breathers, The Gear Box and The Transfer case hoses are secured too. The last picture shows the one am missing the hole too. The one in the middle. I have four secured and there are five tubes. I'm at a loss.. I know you feel my pain.
Thank you very much for your quick response and kind help.

Finally, mystery solved !
Looking at some pictures I took when I bought the truck, I found one with the vent hose intact_not burn, it does go down in a loop.
Look for the arrow on the picture.