Just because the power light is on, doesn't mean it's spinning / active. Most drives nowadays (including externals) go into a low power/sleep mode even when your computer is on after they've been idle for a period of time to save power/wear.
If you want to disable that, check your BIOS settings. Or just unplug them when not in use.
If you want to disable that, check your BIOS settings. Or just unplug them when not in use.