When spotting a red light or similar, I often release the gas pedal, gear down and let the engine decelerate instead of pressing the brake pedal. I was taught that this was more energy efficient for some reason, but I never really understood why. Is thIs true?
I've worked as eco-driving instructor for TCS (Touring Club Suisse), explaining people how to be the most energy efficient while driving a car. I've also spend a lot of time driving a car where you can see the "instantaneous fuel consumption", and I've seen all I write in real life. I've also drived a lot of automatic car, includind Toyota Hybrids with Eco Mode. All the following assumes you drive a car with an electronic injector as opposed to a carburator (this is true for most cars that are less than 20 years old).
The basic rule I teach is: lower revs per minute -> lower fuel per mile. It's not always true, but it's mostly true. Example experimental demonstration.
But there is more. If you coast, the motor uses fuel to stay at idle speed, but when you have the gear engaged, the injector uses an interuption of fuel injection during deceleration. What is important is that the interuption only occures when the rpm is over a minimum (to avoid motor stall).
Another things to look at, is what automatic cars do. Automatic cars are designed to spare the engine and save up fuel. When you are driving downhill, your automatic car will automatically choose the highest possible gear. If you stop pushing the gaz pedal, your automatic car will automatically choose the highest possible gear. And this is what a Toyota Hybrid's Eco Mode will advice you to do. This means that the "use the highest gear possible" is not just an idea of gouvernement mandated experts. It's what the engineers that designed the car want.
But the conclusion is that, energy fuel consumption wise, braking and gearing down both use no fuel. (So long you don't feel your car giggling because rpm are too low)
At the TCS, we advised people not to gear down, because engine braking does not benefit from the anti-lock braking system (ABS), and because it's better to wear down brake pads than the engine. We have been told that the TCS engineers did the math, but I could not find a reference for those calculations.
But this was not true 30 years ago, when cars had carburators. With a carburator, gearing down uses more fuel than braking. But, at the same way, without an electronic injector, driving at low rpm was bad for the engine (because the air-fuel ratio was not allways optimal). And this is probably why your parents' driving instructor taught them to drive that way, and why they tell you to do it.