Tremec Transfer Case breather

[DCPU]

So @Clark Kent posted a great photo on another thread:
Post in thread 'Diff breathers' https://www.theineosforum.com/threads/diff-breathers.12368697/post-1333205454

"This could be the transfer case breather. Front face of the transfer case up the top. Viewable from the left side of the vehicle looking up and rearwards.
Hose goes forward along the top of the transmission then up between the firewall and the back of the engine. Can't follow it to see where it terminates."

So I thought I'd ask Ineos Customer Services if they could shed any light on it.

My question:

1st response:

2nd response:

3rd response:

 

[Blackbox88]

Interesting answers from CS not to helpful
If they would release the promised 3d detailed manual we can look it up ourselves
Maybe would the guys from LeTech know this answer as they have done a lot of work on the grenny.

 

[Jean Mercier]

View attachment 7824397

Waw, it sucks. "We think it goes to ..."

Philippe is probably the French speaking guy who called me after I told Laura that I definitely didn't want to ask my dealer for an answer!
And what did Philippe:
He told me: I give you a number of another Belgian dealer who probably can answer.
I refused, and I am still waiting for an answer after he told me he would chase for it.