I should add that the original A590 PSU did not provide power, so I went ahead with what I suspect is a vintage internal PSU I found lying around that had the same connector modded onto it, which at least gave power to the unit.
To my knowledge the original A590 PSU is wired in such a way that will provide power to the A590 only when the connected Amiga 500/500+ will be turned on.
The Amiga 500/500+ wont boot if an A590 is connected and not properly powered.
Are you 100% certain that your original A590 PSU doesn't work?
I would suggest to try again using your original A590 PSU (and of course turn it on before powering your A500+)
