If there's no current flow, no regulation is possible. You may even damage it when running with nothing connected. You need to connect at least a hard disk or something that permanently draws current.

The old PCS from IBM 51XX era would many times come with a big resistor if you didn’t have a hard drive.

Usually the system wouldn’t turn on if the resistor was missing

Gotcha, thanks a lot! Back to the bench then - with a sacrificial HDD (I fear the PSU may still be faulty).

I wonder: I have lots switching power supplies around me, from modern-ish ATX PSUs to 12 V car battery chargers, USB wall chargers, and bench-top adjustable power supplies. They all work just fine without any load at all, what makes the AT PSUs different?

Just depends on the PSU design. Unlike a wall-plug PSU (chargers etc.), an AT PSU was not designed to be turned on with nothing connected. What happens then depends on how the protection circuit is built.

derSammler wrote on 2020-04-08, 09:53:

If there's no current flow, no regulation is possible. You may even damage it when running with nothing connected. You need to connect at least a hard disk or something that permanently draws current.

There's always some parasitic load. A really shitty SMPS will hit a minimum duty cycle threshold as load decreases where output voltage will start climbing until your retro gear is converted into a smoking ruin. A shitty SMPS will protectively shut down as voltage climbs but helpfully reset and smack your rig in the face again. A not so shitty SMPS will shut down and stay down until it's power cycled or wait more than one cycle before pulsing though limitations of the feedback loop result in some low frequency noise. A good SMPS features a wide range of duty cycles and wide stability bandwidth eliminating no load instability.

I have a few AT power supplied that don't do anything if there is no load. Basically nothing happens you turn on the power like that.

Thanks for the advice and the explanation! I was wary of risking the whole motherboard, but it never occurred to me to connect an HDD.
Indeed, with one HDD the PSU starts up fine and the HDD spins. The voltages are 5.00 V and 10.75 V. After connecting a second HDD the 12 V line goes up to 11.3 V. I suppose even the combined load of two HDDs is not quite enough to put the PSU into its intended operational range.