If you use a SimVim_LCD slave board, you can see (in the configurator) that pins A5, A6, A7 are assigned as power lines:
A5 - Bus1 +Avionics power
A6 - Bus 1
A7 - Bus 2
You can use any of them to control the LCD backlight power.
In the simplest case, if it is just one or two displays, you can directly connect this output, with several resistors in series, to the backlight line + V).
Now, when the BUS voltage drops, the brightness will become dimmer, and then completely turn off.