Don't know if it helps:
The thing looks like a switching mode power supply (should be obvious if you open the box). A common reason for output instability is the feedback loop of the smps / pwm controller. My hint: open the case, try to identify the control loop IC and supporting components, search for datasheets to get an idea of the construction and circuit. Then try to watch the feedback / control loop waveforms and search for worn out components and so on.
It's way more difficult to do without a service manual, but in my opinion still achieveable since it's "just a power supply" and not something really fancy bag of tricks like the Datron 1061 multimeter (without the service manual no way to understand whats happening inside).