It sounds like the only thing missing is a "flaps down" indicator. Right? I agree, you don't need to program an Arduino for that.
So, I'd use those same switches as my cut-offs for the motor as well?
Maybe... It depends on how it's wired. You should be able to "tap into" that switch's logic and possibly use a transistor as an inverter to turn the light on when the motor goes off. You may need some additional logic to hold the indicator on, and then to keep it off when the motor is reversed.
There are various logic circuits such as "and gates", "or gates", "inverters", and "flip-flops". These don't need to be programmed with software. Their function (and combined function) depends on how they are wired. If the logic is fairly simple, and there's no "counting" or math, logic chips are usually easier.
When the circuit starts getting complicated, it becomes easier to do it in software (with a microcontroller).
Note that most logic circuitry (as well as the Arduino) runs off 5 Volts. "Converting" a 12V signal from a switch down
to 5V only takes a couple of resistors. But, converting up
to run a 12V lamp (if you don't want to use an LED) requires something like a MOSFET or transistor or relay.
Or, maybe there's an unused terminal on the switch (if it has normally-open and normaly-closed terminals).
Or, you may need to use an additional similar switch.