I just repaired a Switch Lite, it uses the same LCD driver IC, and the Rohm part number BD8316GWL you found is correct. It is laid out in a 4x3 grid with one ball being notably smaller than the rest, giving it the 11 pins.
Does anybody have identification on this component? I tried tracking it down, there's two references to 8316 and 6T59 - so I figured maybe it's the BD8316GWL but the dimensions are wrong and it has 11 pins opposed to the one here which is only 9 pin(?). I found an aliexpress page selling them and I've ordered some, so I can better see those at least when they arrive.