When replacing the lower intercooler hose I dislodged what looked like a suspension air hose that ran along the top of the chassis and then went up the side of the radiator.

The other end of the hose runs towards the transfer case and has a green connector on it. the connector is not connected to anything

I am assuming that this is a breather hose, only I'm not sure if it is from the transfer case or the gearbox or somewhere else. Any ideas what it should be connect to and where I'm likely to find the loose end?