With respect to the hardware and the USB HID protocol (i am assuming you are using a USB keyboard), the PAUSE key is no different than any other key on the keyboard (except the modifier keys), with the keyboard just sending the scan code of the respective keys being pressed/hold down at the moment the keyboard is being polled/scanned. (Scan codes are not the same as key codes. Scan codes are what the HW deals with, and loosely correlate with the location of a key on the keyboard regardless of what symbol is printed on a key cap -- rare-ish exceptions not withstanding --, whereas key codes are what the scan codes are translated into by the OS.) I have no experience with low-level keyboard tinkering in Linux, but perhaps look for a way to map scan codes instead of key codes. And for the same reason i can't say if the specific PAUSE key behavior you observe is due to the kernel/OS, or the result of some other software component or a quirk of the key mapping software itself... :-(

elgonzo‭ I use my laptop's keyboard — but since I read that touchpads may be USB or PS/2, I reckon a laptop's keyboard might also be so?

Yes, in most cases the keyboard is either connected by an (internal) PS/2 interface for old(er) laptops, or USB for modern-ish laptops. Seldomly -- if at all - you will find a laptop that uses a different interface for its integrated keyboard, simply because that would demand from the manufacturer to add yet another controller IC to the BOM and to provide matching (custom) drivers for the supported OS's.

(Just to make clear: I am NOT talking about how the physical keyboard module is electrically connected with the laptop's circuit board, but about the keyboard interface to the chipset/CPU. If the keyboard controller were to sit on the laptop circuit board, the electrical connection between keyboard module and circuit board is entirely defined by how the concrete keyboard controller chip being used wants/needs to be connected with the key matrix, something that is entirely unrelated to how the keyboard controller interfaces with the CPU/chipset.)

elgonzo‭ You might want to see the edited answer. Unfortunately I could not find a way to determine the PS/2 mode of my keyboard.

Quasímodo‭ i found very little about PS/2 mode 3 aside from a few forum posts talking about old terminal / workstation keyboards. Wich leads me to believe that PS/2 mode 3 was/is an protocol not used in standard PCs, although i am not 100% certain due to not being able to find any authoritative documentation about this mode. :-(