Is it possible for DT024CTFT to perform "Write Display Brightness"?
Backlight is controlled by pins "A" and "K", pins 40 & 41, not through the ILI9341.
You have different ways to control the backlight:
1) No control over brightness, via a resistor hard wired.
2) A PWM signal generated by your micro, or through a light sensor.
Please refer to the CAT4139 for controlling backlight.