My Design Idea (DI), “Flip ON Flop OFF for 48-VDC systems,“ was published and referenced Stephen Woodward’s earlier “Flip ON Flop OFF” circuit. Other DIs published on this subject matter were for ...

Toggle, slide, push-pull, push-push, tactile, rotary, etc. The list of available switch styles goes on and on (and off?). Naturally, as mechanical complexity goes up, so (generally) does price. Hence ...

I'd guess you are looking at a cap failure in the original PSU. 386 era is what, early 90s. 30+ years is a good run. If a replacement PSU doesn't have a switch, you could always hook it to a surge ...