Not too bad a picture ;-) to make really good ones it takes macro lenses and a stable setup.
Anyway, back to the problem.
I don't think that board has anything to do with the backlight other than being a passthrough. If U49 is the chip you indicate then you will have to look elsewhere. The board appears to be multi layer so we can't trace the tracks but I am thinking the controller is most likely on the main board.
Next test would be to find out if the + line for the LEDs is connected to any other socket, the - will most probably be a common ground and unswitched. If it is, then you will have to trace where that goes.
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