You probably can't, at least inside the Amiga…

What the board can do, is to control an ATX power supply (example: AT backplane, ATX power supply with AT adapter, you connect a regular power button + the green and purple wires to the right pins of the JP3 connector, and you get it to work like a regular ATX computer) - but it probably can't turn off on its own if something else (the Amiga, or in the above example if you connect the green wire to a classic "AT" power switch as normally done) is giving it power…

For SBCs used with ATX power supplies usually an additional connection from the Backplane to the SBC is needed.
ISA and PCI Slots do not carry the 5V standby power line needed to start the system.
The connections differ between manufactures.
While Advantech uses a 3 wire connections others like Bluechip use 5 pin connections.
Be careful messing around with these connections.
Fried an Advantech SBC last nicht while trying to connect it to a Bluechip backplane via wrongly soldered adapter.

Honestly this SBC is connected only to the isa slot without any other connections and it works perfectly. Except that I would like to turn it off, but I'm afraid that it can't be done

then put power management in bios to max saving. and a plug power meter will tell you if it helps.