Mac won't access 4 TB Seagate USB drive
Short version: I have an old Mac with old-spec USB ports that only supply a limited amount of power to the connected device. That's enough to drive the circuitry (hence the console report) but not enough to spin up the physical disk. Of course, this is not a problem with thumb drives.

Solution: connect the drive through a powered hub, to provide the extra juice that's not coming from the Mac. It's possible that an older powered hub wouldn't work. Fortunately, current models are quite cheap.

This is arguably a duplicate of this question, where the problem is the same. But it's an old question, a bit of a mess, and the best solution offered (use a special cable to feed extra power) is not practical for most people.