When a passenger gives constant advice or orders to the person behind the wheel. The Henpecked Husband's wife or mother-in-law will do this a LOT. The Logical Extreme is a passenger who actually grabs for car controls (usually the wheel). In Real Life, there are legal consequences for this.
Yusei constantly gives this to Crow in the 2008 Yu-Gi-Oh! 5Ds show. Which Yusei tends to always show that Big Brother Instinct attitude of his. And that he had more experience turbo dueling than his buddy; Crow.
It's a Mad, Mad, Mad, Mad World - Milton Berle's character has his mother-in law (Ethel Merman) taking this role to heart in a race to buried treasure. She bellows "We're the ones in the Imperial and we're in last place?" Later, she continues barking orders to different drivers in different vehicles.
Quite literally in Cannonball Run 2 when two of the characters participating go in a car with a very visible driver seat that has a orangutan suppose chauffeuring them. Turns out they're really driving the car from the backseat.
Loki: Don't hit the buttons, press them gently. Thor:[hitting the buttons harder] I am pressing them gently! [...] Loki: Look, why don't you let me take over, I'm clearly the best pilot. Thor: Is that so? Of the two of us which one can actually fly? [...] Loki: Now they're following us. [shots] Now they're firing at us! Thor: Yes, thank you for the commentary, Loki! It's not at all distracting!
As this is a British show, "the pavement" means the sidewalk.
Happens all the time on The Amazing Race when teams are tasked with driving themselves. As a bonus, because of the way the camera crew positions themselves in the car, the non-driving teammate is always positioned directly behind the driver.
The role can occasionally be played by the Guy in Back, reminding the Ace Pilot not to burn up all of their fuel, or warning him of enemies coming up on their six. Of course, this is part of his job, but too much implies a lack of trust between them, or a certain fresh inexperienced quality about the guy in back.
A sketch on the British radio show Week Ending featured the car itself as this. The Austin Maestro featured a voice synthesiser to issue warnings to the driver - a supposedly amazingly futuristic innovation which was universally derided by the public. The sketch portrayed the synthesiser as a Backseat Driver which continually nagged and hassled the driver, annoying and distracting him so much that he ended up wrecking the car.
The Warhammer 40,000Gaiden GameGorka Morka had a skill called Backseat Driver. When a character with the skill was in a vehicle the driver could use their stats instead of his own for some driving checks.
Implied — some vehicles, notably the Toyota Yaris, have the instrument cluster mounted in the center of the dashboard, between the driver and front passenger. While there's no proof that any manufacturer's implementation of this design is to explicitly support backseat drivers (though it does simplify manufacturing left and right hand drive models), there's no proof that it isn't either.
The valid case of the trope is a driving instructor to assist new drivers. Their vehicles are equipped with passenger-side controls in case the inexperienced driver is about to make a collision.
Not this trope, but cars like the page image did exist early on in automotive history.