There are "brightness control" with the car dimmer came up before. I am not sure what the solution is.
I think dimmer control "maybe" deferent among cars. Some may use POT while other may use PWM. For Toyota, it use POT on the - wire. On monitor Lilliput I have no clue.
Anyway, whatever your installation is, if you plan in advance, you can always relocate the IR sensor on the monitor to a place you can use remote control with it.