Some time passed and I figured that I had to save the 4D Systems backlight for this project to be successful. Studying the display datasheet, I've found that it has a command that can turn off /turn on the backlight, and I figured that I needed just some kind of pulse to get it to work. What could be the source of this pulse?

Of course! A PIR sensor! Quickly I bought one from the internet and when it arrived I've put into practice the plan. Added new connections, added new inputs to the Arduino, implemented the codes into the logic, and it worked successfully! Now it shuts down the backlight after 10 seconds without any signal from the PIR, and as soon as the sensor picks something, it turns the backlight back on! Success!