Thanks mate.
The ID is around 7.5-8mm. The OD is 13mm. The hose definitely didn't have oil in it, as there is no trace of residue.
After cleaning up the hose, I could read "GATES ERS 117 0686 23:54 JK" on it (those are my best guess, as the markers aren't in the best condition). Looking through the gates catalogue, there is no hose with that ID nor any that look like this for the SY Territory.
I just had a thought, could it be the front diff breather tube?