Check the schematic. The backlight is permanently connected to power supply via resistor R8, so there is no way to control it. You may modify the board by removing R8 from its position and soldering it in series with an NPN RET (bipolar transistor with build-in resistors, like PDTC series) Another possibility is to use some small NMOSFET, like BSS138, but then you must also add another resistor of 10..100k between gate and ground. You may then control the base/gate of a transistor with some PWM timer output.
