So I visited Al Habtoor today, explained the situation to them. They did a complete inspection (test drive, OBD, etc.) and suggested that the differential is the root cause. They also ruled out wheel bearings as a cause and told me that those would make a consistent noise.
Suggested repairs by them includes replacement of solenoid valve, free wheel switch and hoses. If that does not fix the problem then the actuator and all 4x4 switches need replacement.
The leak in differential was a false alarm, it was some leftover WD40 from the timing belt replacement job 😅.
My personal experience with Al Habtoor was a good one. They were professional and quite helpful. Have to give credit where it's due.
My Pajero is still under Al Futtaim warranty (Automall purchase), so I will be visiting them to get the fixes done. I have already visited Al Futtaim Auto Care Centre twice in the past for this particular issue, both times they said "we cannot fix what we cannot observe". So I am under immense pressure of recreating the noise during test drive when I will visit them again. If the noise does not occur during test drive then I will insist on the video being proof of the problem (already tried in the past) and of course diagnosis from the official Mitsubishi Service Center Al Habtoor.
@Marek @Frederic I found a post on an off-roading forum about this exact issue where people have (over) analysed this issue. I am pasting the technical explanation from that post to shed some more light on this issue:
BTW while driving today I was able to turn off the noise again by switching from 2H to 4H.
I will do some more research as well as tinkering and hopefully get the car to make the noise on command. That would make my life much easier when trying to explain this fault at the service centre. Would appreciate any tips to recreate this sound when I want for demonstration purposes.
I will keep you guys updated. Thank you!