My experience with PSU testers has been go/no-go & is all that I needed to know.
My own personal theory of PSU failure is all or nothing. They use switching electronics for efficiency and if it fails ... then there is nothing. This is all I have needed to know to decide if the m/b has failed or the PSU. Compared to buying a PSU, CPU, m/b, or the simple minded PSU testers the tester is the least expensive. Even if you plan on returning one of the other parts, it is still far less of a PITA than dealing with RMAs.
Having said that, where is the click click clicking sound coming from? The fan? Did you hear the clicking when the PSU was still installed in the computer? And, plugging in even an old HDD is a good idea to add a load ... try with & without the "load".
This will sound absolutely absurd to many & incredibly dangerous, but can you stick something into the air exhaust to stop the fan from spinning? Ok, something insulated and for no longer than absolutely necessary to tell if the clicking stops? Or with a little help from someone, figure out how to stop the fan before power up (you holding the ... whatever to block the fan) & your assistant doing the plugging into the tester.