Thanks @Chedwin
I may have to cut the wall to figure out the spot where the water is coming in from outside. There is a concrete foundation wall behind the leaky HT wall (the left side wall in the picture below) and I suspect that the rain water is penetrating the foundational concrete wall.
There was no leak before. I am trying to be positive about it but it is very frustrating indeed 😀
Possible solutions include pinpointing where the water is coming in from outside and getting it sealed. I may also have to paint the concrete wall inside, with a water sealant paint.
Oh well!