False digital triggers when powering Nano from a car

I’m working on building a few projects that will be powered from a cars 12-14 volts power source. I’ve simplified this project to explain the issue I have found. I’m using the car to power a 7.5v regulator and then send it’s regulated output to a Nano. The Nano’s digital pin 7 is setup with the internal pull-up resistor. With the pin 7 wire and the cars power and ground ran through the same multi conductor wire the digital input will randomly trigger false positives. I have also tested this basic circuit on a bench with 2 feet of multi conductor and a car battery. One obvious solution is to move the pin 7 wire out of the multi conductor and away from the cars power source. I would like to find a more reliable solution. In the real world there will be several power sources in a vehicle that would need to be avoided with this design. One thought I had was to place an external pull-up resistor at the end of the multi conductor wire run. I would appreciate any input on other design solutions.

void setup() {

Serial.begin(9600);
pinMode(7, INPUT_PULLUP);
}

void loop() {

int buttonVal = digitalRead(7);
Serial.println(buttonVal);
}

A capacitor from the Arduino input to ground might help. (Maybe 0.1uF). If the glitch is getting-in through the regulator, a bigger capacitor (maybe 1000uF or more at the across the 7V supply may help.

I would consider the cap and a stiffer pull-up. If it is acceptable for the application, consider some form of debounce as well. You may need to do everything, including pull the wire out of the bundled cable.

Cars are noisy places.

I added a capacitor from the Arduino input to ground on my bench setup and it seems to have removed the false triggers. Hopefully this will hold true when I test the project in a vehicle. Before adding the capacitor the regulators output looked smooth with my scope readings. Can someone explain the capacitors function after the voltage regulator. Do the regulators create noise that is then sent to the Nano causing the false trigger? I was surprised the circuit would false trigger even when bench tested with a car battery (no alternator noise). Is a smaller 0.1uF capacitor better for noise suppression than say a 4.7uF?