fyi to all, the apple diagnostics (be they the Apple Hardware Test or the Apple Service Diagnostics) are located in a hidden folder
/System/Library/CoreServices/.diagnostics/
That folder is present on a mac shipped from apple, but may be overwritten if you have to reinstall your OS, since that's an OS folder. It's possible to reinstall it, but it's a bit of a hassle to find and to get correctly reinstalled. If it's present but not selectable or does not start, it's probably not blessed (similar to blessing a regular OS startup volume), and may require a terminal command to fix.
IIRC, it will show up in the boot picker, when you hold Option at startup. It may not be named logically, and may show up as "EFI" or "EFI Boot".
You can also try holding "A" instead of "D".
