Thanks, mate!
I'm thinking about ordering this from AliExpress:
PSU Tester - AliExpress
Video tutorial / review:
View: https://www.youtube.com/watch?v=Ukcmp2EkYA0
It's quite cheap and seems to be rather accurate. But do let me know if you've other suggestions.
These are quite good actually, you'll want one that can actually read individual voltages as that one does - but I would say don't expect it to last forever!
It will certainly help clarify the issue you are encountering, just be wary for future reference that the PSU testers don't guarantee if the PSU is working or not. They just look for something obviously wrong, and if they pass, doesn't mean they are OK, but if they fail, it definitely means there is a problem.
The other side of the PSU testers to consider is they only check voltages at idle, whereas many PSUs throw out problems when itself or other components are put under load. So a PSU tester can pass a PSU normally in this scenario, but once the PSU comes under load back in the system, it's voltages start fluctuating for example.
They are great and handy tools, just come with their precautions.