Useful information, FYI. I posted it on OldNewThing, so here it is slightly modified
Almost all of the USB to PS/2 mouse adapters are purely rewiring, but one isn’t : HIDMan (on Github). That will accept USB keyboards and mice (up to five buttons) and output PS/2 (or serial mouse). It can be fairly easily made at popular PCB fabrication places as it’s open source. I’ve recently had a few made and they’re excellent, enabling me to use a modern remappable USB keyboard[1], and will help if I want move on from my Logitech MX518, probably the last multi button mouse to support both PS/2 and USB directly.
To go the other way, there are many PS/2 to USB adapters on the market, but they’re of varying quality, don’t tend to stay in manufacturer catalogues, and typically contain one of only a few basic chips/USB IDs, but you can’t see what chip is in them so the best advice is normally ‘buy Startech’. The reliable way is likely to be to buy a TMK keyboard protocol converter (also supports mice), again the firmware and hardware are open source.
One good reason to buy a TMK (I’m going to, just haven’t yet) is for mice with more than three buttons. Whilst USB does support multi buttons natively, all the PS/2 to USB converters I’ve tried so far don’t, I had to use real PS/2 to see five buttons enabled. TMK claims they support five button mice so I’ll be buying one to handle the slightly ridiculous signal path of USB keyboard/mouse->HIDMan->fancy PS/2 KVM[2]->TMK converter->USB (yes, the PS/2 KVM does also plug directly into PS/2 only systems, one system using a serial mouse and AT keyboard, and a Sparcstation using a cheap F1DE083UK[3] PS/2->Sun converter).
If you don’t want to do TMK, note my experiences with seeing what adapters a MiSTer FPGA system supported PS/2->USB mice was (may have changed now):
Works :
0557:2221 (unmarked adapter). Identifies as : Aten Winbond Hermon
0557:2221 Branded Aten UC-10KVM. Same chipset as unmarked adapter!
04b4:2324 (unmarked adapter) Cypress Semiconductor USB PS/2 bridge
Non working :
0d3d:0001 Tangtop Ltd HID keyboard adapter (the square one. Not a surprise, it is only designed to support keyboards)
13ba:0018 PCPlay Barcode PCP-BCG4209
13ba:0018 another unmarked adapter.
Do you feel lucky?
[1] My Unicomp hardwired Dvorak buckling spring keyboards died. The choice is then repair them (will take a while, fiddly), ship a new one from the US (slow, expensive), or buy a HIDMan and a programmable keyboard off the shelf - current solution. The HIDMan is great, the Montech TKL I bought less so - if you keep replugging it it sometimes forgets what keys do, or its lighting settings.
[2] A decent second PS/2 KVM can be very substantially cheaper than a USB one, is more appropriate if you need to control a lot of old systems, and you may already have gathered the expensive cables from other KVMs. Let's just say this home study has substantially more than one computer (or even ten) and is pretty much a 90s systems museum..
[3] Search for 'Belkin Omniview universal USB to ps/2 adapter for Sun' on ebay UK. It's there, is a tenner, and works. Had difficulty getting VGA->13W3 working so used a separate passive adapter for that.