On a manual transmission, when is double-clutching required to change gears?

49 CFR 383.111(a)(5) (Shifting); AAMVA CDL Manual Section 2.3.1, p.2-9

Double-clutching lets the engine and gears match speed without gear-on-gear grinding, which matters on big-rig transmissions that lack synchronizers to do that matching automatically. Using it when it's not needed, or skipping it when it is, can damage the transmission or cause a missed shift at the worst possible moment, like merging onto a highway. Knowing which transmissions require it is core knowledge-test material for every Class A driver.