So, as it turns out, getting the first generation Apple Wireless keyboard from 2003 to talk with modern Linux systems is a little tricky.
It doesn't seem to use a protocol that's entierly supported these days, and as a result, it either shows up in bluetooth managers, but can't be paired,
or it doesn't show up at all.
After some research and headscratching I did find a way to make it work though. The whole trick is to use bluetoothctl in the terminal, and a 6-digit pin.
Run bluetoothctl in a terminal and type the following:
power on
agent KeyboardOnly
default-agent
pairable on
Turn on the keyboard. Wait for the light to start flashing. This indicates it being in pairing mode.
Enter the following command:
scan on
Wait for the keyboard to appear in the terminal. It's a MAC-address followed by either "Apple Wireless Keyboard" or whatever your keyboard has been renamed to.
Copy the MAC-address and write this command in bluetoothctl:
connect *MAC-address here*
Blindly type a 6-digit pin-code on the keyboard, for example 123456, then press Return.
bluetoothctl should now display a pin-code prompt, where you input the same code as you typed on the keyboard.
[agent] Enter PIN code:
Bluetoothctl should now connect the keyboard, and show the following:
[CHG] Device 00:0A:95:33:33:33 Paired: yes
[CHG] Device 00:0A:95:33:33:33 Connected: yes
[CHG] Device 00:0A:95:33:33:33 Modalias: usb:xxxxxxxxxxxx
[CHG] Device 00:0A:95:33:33:33 UUIDs: xxxxxxxxxxx
[CHG] Device 00:0A:95:33:33:33 UUIDs: xxxxxxxxxxx
[CHG] Device 00:0A:95:33:33:33 ServicesResolved: yes
Connection successful
Enter the following commands in bluetoothctl to stop the scanning and pairing process:
scan off
pairable off
Confirm the keyboard is paird by typeing the following command:
paird-devices