They always engaged or do you engage them?
Both, see how simple this all is???
Actually most of the ones you might install or encounter are automatic. When you go around a corner, one wheel goes farther than the other and has to turn faster. That is why you have a differential, so the wheels can move at different speeds.
But, due to the design, if one wheel loses traction, all the power goes to it. That is called an "open" differential.
A locking differential works in a couple of different ways. The clutch type have slip clutches inside that lock the two axles together so they have to turn at the same speed.
But, when you go around a corner, the load exceeds the clutch strength and they slip letting the wheels go at different speeds.
In a slick place, or with one wheel off the ground, some of the power still goes to the good wheel to the limit of the clutches.
Others will let small amount of differences slide by, but when the different wheels start trying to turn fast than a set speed, they lock up with gears or cams. The are better for bad places, but are not as nice on the highway.
All those are automatic, and you don't have to do anything to turn them on or off.
However, there is an Australian outfit that makes one that is fully open for driving normally, and then you flip a switch, and air pressure from a small onboard compressor slides a locking collar over inside the rear end and locks the axles together.
So, you have either automatic ones or manual ones and all kinds of flavors.
Don't even bother asking which is better. Wait until you get your truck, and post a separate thread for opinions.
You will get plenty.