Not only is engine braking a technique that will make you a bit safer driving down a mountain pass, the science behind it can actually save you more fuel over just coasting in neutral.
Years ago I took a road trip with my then-girlfriend, now-wife down to North Carolina. We decided to take what is considered "the most scenic roadway" in America, the Blue Ridge Parkway. Coming around the blind mountain turns in a 2003 Ford Windstar was no fun. Living in relatively flat New Jersey I had never experienced driving in these kinds of conditions before.
I just assumed that if you wanted to slow down, you use the brakes. I wish I had seen this video from our friends at Engineering Explained before I took that drive.
Which is more efficient? It depends.
As Jason explains here, there are circumstances where leaving the car in gear and engine braking uses less fuel than shifting into neutral, and he demonstrates it with a hilly drive and a gauge showing his real-time MPG.
But if you're going down a hill, then up another hill one right after, you'd use less gas if you went down in neutral because you'd gather more momentum to push you up instead of using the engine to accelerate. It's kind of like a roller coaster, he says.
It's good advice. Once I learned the hard way about engine braking, my trip to California was much more enjoyable cruising through the mountains.