Something like this?

You can figure out an exact voltage rail wiring on any motherboard by checking continuity between a bus connector and the PS header of interest. There should be typical +5/12, -5/12 voltage rails, a +5V_SB might exist on that model, at least the IBM PSU, that I restored recently, had it.

I did that but the MCA bus doesn't have -5V. The same goes for the PW_GOOD and the +5VSB pins.
http://www.interfacebus.com/IBM_MCA_PinOut.html

Got this picture. Is the ON/OFF signal identical to the PS_ON signal of ATX?

Model 33 has the same pinout.

Try tracing ON/OFF signal pin to the power switch, if it connects to ground when the switch pressed, then you can connect PS_ON wire to that pin.

This is where I face the next problem: the computer is missing the power switch assembly.
I also don't know the pinout of header J19 to locate where the power button goes. I measured what I could.

Correction, it's probably this switch assembly. I only assume because of the number of pins.

J19 connector is just a front panel header for activity LEDs, power switch and misc. stuff, that can be absent on your model. I think ON/OFF signal pin might directly connect to one of the J19 header pins, but you can bypass J19 for the moment. Connect ATX PSU voltage rails to J18 and J20 connectors accordingly (don't connect anything to the "ON/OFF signal" pin) and try to power it on by shorting PS_ON wire to ground, PC should turn on, unless it has some undervoltage protection circuit on the MB, comprising from OP-AMPs/comparators.

I'll do the wiring and report back. Thank you!

Alright, it's running now so I'm not going to use the ON/OFF signal pin.
It started with date and time error (00016300) but no options to set it. Any suggestions?

Never mind, startup disk required. It's true what others wrote about these PS/2s: they are a challenge.

They are, believe me. My first PC was an IBM 8590 XP, imagine having to deal with their technical issues with no prior experience with PCs. Nothing was compatible with the system: PSU, MCA bus, RAM (parity only), cache RAM for HDD (proprietary), floppy drive, hard drive was SCSI and you cound't just swap it for a higher capacity quieter model, because it required a special BIOS setup partition on it, it had 2 sockets for 486 CPUs on a separate CPU board, so on and so on. You could also forget about the sound card option completely.

All's well that ends well. The 2.88 drive worked fine even though it was super dirty before cleaning.
Since I don't have a 50 pin SCSI HDD it's as far as I go for now.
Believe it or not I love these computers with all the proprietary parts that give me a hard time.
I still have parts missing, like the 212 MB SCSI HDD, the switch assembly, the back cover and all these parts cost an absolute fortune. I'd never spend hundreds of dollars for these, it's highway robbery. MCA sound card? No way for $900 that's crazy. But it's nice to own an IBM machine even if it's not 100% original.
Thank you for all the help. I'll spend more time with it when I get a SCSI HDD.