Is Double Clutching a real thing?

Yeah, it's a thing. Not a particularly necessary or useful thing, but it's a thing. And something instructors make you show you can do during the road test. My instructor just had me show I knew how to double-clutch a couple of times, and let me float the rest of the test. The idea behind it is that the RPM of the output gears in the transmission need to match the speed of the input shaft relative to the gear selected; the "gear" is a bridge, the ratio that matches the input shaft to the output shaft. The first use of the clutch is to get the truck out of gear so the bridge can be removed, usually at the high end of engine RPM while upshifting for accelerating or cruising, or the low end when downshifting. The second use of the clutch, either with the engine returning to idle or being punched-up to higher RPM, is to introduce a little pause before operating the shift lever. Seriously, it does basically nothing. The truck won't go into gear if the input & output RPMs aren't pretty close. There's no syncrhomesh in a heavy duty transmission to help match the speeds of the shafts when the clutch is engaged. The clutch barely provides any additional wiggle room. Shifting too quickly is the problem double-clutching addresses. Knowing the appropriate road speed for the RPM for the gear for a given truck to float the gears, or just having a feeling for the timing for floating gears and which gears you can skip is far less work and far less risk of screwing-up the timing. The clutch is mostly just good for getting the input shaft to slow or stop to put the truck into a starting gear, or for unbinding it if the RPM is too high or low & binding the gear. And making your left leg strong.